Arithmetic groups and their generalizations: what, why, and how
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2008
[Somerville, MA] International Press |
| Schriftenreihe: | AMS/IP studies in advanced mathematics
43 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. 183-243) and index |
| Beschreibung: | XVII, 259 S. Ill. |
| ISBN: | 9780821846759 0821846752 9780821848661 |
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| 020 | |a 9780821846759 |c alk. paper |9 978-0-8218-4675-9 | ||
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| 100 | 1 | |a Ji, Lizhen |d 1964- |e Verfasser |0 (DE-588)120496348 |4 aut | |
| 245 | 1 | 0 | |a Arithmetic groups and their generalizations |b what, why, and how |c Lizhen Ji |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2008 | |
| 264 | 1 | |a [Somerville, MA] |b International Press | |
| 300 | |a XVII, 259 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a AMS/IP studies in advanced mathematics |v 43 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Includes bibliographical references (p. 183-243) and index | ||
| 650 | 4 | |a Arithmetic groups | |
| 650 | 4 | |a Linear algebraic groups | |
| 650 | 0 | 7 | |a Arithmetische Gruppe |0 (DE-588)4255663-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Arithmetische Gruppe |0 (DE-588)4255663-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-3833-3 |
| 830 | 0 | |a AMS/IP studies in advanced mathematics |v 43 |w (DE-604)BV011103148 |9 43 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016721056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016721056 | ||
Datensatz im Suchindex
| _version_ | 1804137992792571904 |
|---|---|
| adam_text | Contents
Chapter
1.
Introduction
1
Chapter
2.
General comments on references
5
Chapter
3.
Examples of basic arithmetic groups
7
3.1.
Z
as a discrete subgroup of
К
7
3.1.1.
Poisson
summation formula
8
3.1.2.
Riemann
zeta
function
8
3.2.
Z and lattices in R™
9
3.2.1.
Lattices in R
10
3.2.2.
Sphere packing
11
3.2.3.
Poisson
summation formula for lattices in R
12
3.2.4.
Weil-Siegel formula
13
3.2.5.
Voronoi formula
13
3.2.6.
Generalizations of the
Poisson
summation formula
14
3.3.
The modular group
51,(2,
Z)
15
3.3.1.
Fundamental domain of 5L(2,Z) in the upper
half plane
15
3.3.2.
Reduced quadratic forms and reduction theory
16
3.3.3.
Generators of SL(2,Z)
17
3.3.4.
Volume formula for modular curves and locally
symmetric spaces
17
3.3.5.
Moduli space of lattices
17
3.3.6.
Compactifications
18
3.3.7.
Deformation retraction to co-compact subspaces
19
3.3.8.
Geodesic flow, continued fractions and symbolic
dynamics
19
3.3.9.
Congruence subgroups
20
3.3.10.
Dirichlet fundamental domain
21
3.3.11.
Finite generation of discrete groups
22
3.3.12.
Arithmetic Fuchsian groups
23
3.3.13.
Characterization of arithmetic Fuchsian groups
23
3.4.
Spectral theory of
Г Н
24
3.4.1.
Weyl law
25
3.4.2.
Spectral decomposition
25
3.4.3.
Discrete spectrum and Selberg s ^-conjecture
26
3.4.4.
Selberg trace formula
27
viii CONTENTS
3.4.5.
Generalized Weyl law
28
3.4.6.
Phillips-Sarnak conjecture on cusp Mass forms and
spectral degeneration
28
3.4.7.
Counting lengths of geodesics-the generalized prime
number theorem
29
3.4.8.
Modular symbols
30
3.4.9.
Selberg
zeta
function
31
3.4.10.
Scattering geodesies and generalized
Poisson
relation
32
3.4.11.
Modular forms and Maass forms
33
3.4.12.
Automorphic representations
34
3.4.13.
L-functions
35
3.4.14.
Automorphic forms on
adele
groups
35
3.4.15.
Converse theorems for L-functions
36
3.4.16.
Applications of modular forms
36
Chapter
4.
General arithmetic subgroups and locally
symmetric spaces
37
4.1.
Algebraic groups
37
4.2.
Definition of arithmetic subgroups
38
4.3.
Hubert modular groups
39
4.4.
Congruence subgroups and the congruence kernel
40
4.5.
Arithmetic subgroups as discrete subgroups of Lie groups
41
4.6.
Zariski density of arithmetic subgroups
42
4.7.
Symmetric spaces
43
4.8.
Non-Riemannian symmetric spaces
45
4.9.
Locally symmetric spaces
45
4.10.
Space forms
46
4.11.
Compactness criterion for locally symmetric spaces
47
4.12. Siegel
sets and fundamental sets
48
4.13.
Reduction theory for arithmetic subgroups
49
4.14.
Precise reduction theory for arithmetic subgroups
50
4.15.
Metric properties and Q-rank of locally symmetric spaces
51
4.16.
Volume spectrum of locally symmetric spaces
52
4.17.
Maximal arithmetic subgroups and automorphism groups
53
4.18.
Counting of volumes of hyperbolic manifolds
54
4.19.
Counting of subgroups by index
54
Chapter
5.
Discrete subgroups of Lie groups and arithmeticity of
lattices in Lie groups
57
5.1.
Crystallographic groups and
Auslander
conjecture
57
5.2.
Lattices in
nilpotent
Lie groups and
Margulis
Lemma
58
5.3.
Lattices in solvable Lie groups
60
5.4.
Lattices in
semisimple
Lie groups
61
5.5.
Characterization of arithmetic groups
62
5.6.
Non-arithmeticity of lattices in rank
1
cases
63
CONTENTS ix
5.7. Arithmeticity
of lattices in rank I cases
63
5.8. Linear
discrete subgroups and Tits alternative
64
5.9.
Reflection groups g5
5.10.
Discrete groups related to
Кас-
Moody groups
and algebras
65
5.11.
Infinite dimensional Lie groups and discrete groups
associated with them
66
Chapter
6.
Different completions of
Q
and 5-arithmetic groups over
number fields
69
6.1.
p-adic completions
69
6.2.
5-integers
69
6.3.
5-arithmetic subgroups
70
6.4.
^-arithmetic subgroups as discrete subgroups
of Lie groups
70
Chapter
7.
Global fields and 5-arithmetic groups over function fields
73
7.1.
Function fields
73
7.2.
Global fields
73
7.3.
5-arithmetic subgroups over function fields
74
Chapter
8.
Finiteness properties of arithmetic
and 5-arithmetic groups
75
8.1.
Finite generation
75
8.2.
Bounded generation
76
8.3.
Finite presentations
77
8.4.
Finiteness properties such as FP^o
77
8.5.
Cofinite universal space for proper actions
and arithmetic groups
78
8.6.
Finiteness properties of arithmetic subgroups
79
Chapter
9.
Symmetric spaces, Bruhat-Tits buildings
and their arithmetic quotients
81
9.1.
Flats in symmetric spaces and the spherical Tits building
81
9.2.
Bruhat-Tits buildings
83
9.3.
Action of 5-arithmetic subgroups on products of symmetric
spaces and buildings
83
9.4.
CAT(0)-spaces and CAT(0)-groups
84
9.5.
Reduction theory for 5-arithmetic subgroups
85
Chapter
10.
Compactifications of locally symmetric spaces
87
10.1.
Why locally symmetric spaces are often noncompact
87
10.2.
Compactifications of symmetric spaces
87
10.3.
Limit sets of Kleinian groups and Patterson-Sullivan
theory
89
10.4.
Compactifications of locally symmetric spaces
91
10.5.
Compactifications of Bruhat-Tits buildings
92
x
CONTENTS
10.6. Compactifications
for ^-arithmetic groups
93
10.7.
Geometry and topology of compactifications
94
10.8.
Truncation of locally symmetric spaces
94
Chapter
11.
Rigidity of locally symmetric spaces
97
11.1.
As special Riemannian manifolds
98
11.2.
Local and infinitesimal rigidity of locally
symmetric spaces
98
11.3.
Global (strong) rigidity of locally symmetric spaces
99
11.4.
Super-rigidity of lattices
99
11.5.
Quasi-isometry rigidities of lattices
100
11.6.
Rank rigidity of locally symmetric spaces
102
11.7.
Entropy rigidity of locally symmetric spaces
and simplicial volume
102
11.8.
Rigidity of Hermitian locally symmetric spaces
103
11.9.
Rigidity of pseudo-Riemannian locally symmetric spaces
105
11.10.
Rigidity of non-linear actions of lattices:
Zimmer
program
106
11.11.
Rigidity in
von
Neumann algebras
109
11.12.
Topological rigidity and the
Borei
conjecture 111
11.13.
Methods to prove the rigidities
112
11.14.
Dynamics, flows on locally symmetric spaces
and number theory
113
Chapter
12.
Automorphic forms and automorphic representations
for general arithmetic groups
115
12.1.
Automorphic forms
115
12.2.
Boundary values of eigenfunctions and
automorphic forms
116
12.3.
Spectral decomposition
117
12.4.
Weyl law
118
12.5.
Counting of eigenvalues for a tower of spaces
118
12.6.
Quantum chaos
119
12.7.
Arthur-Selberg trace formula
120
12.8.
Selberg
zeta
function
121
12.9.
Counting of lengths of geodesies and volumes of tori
122
12.10.
L-functions of automorphic representations
122
12.11.
Meromorphic continuation of
Eisenstein
series
123
12.12.
Constant term of
Eisenstein
series
124
12.13. Langlands
program
124
12.14.
Spectral theory over function fields: an example
125
Chapter
13.
Cohomology of arithmetic groups
127
13.1.
Cohomology groups
127
13.2.
L2- and ^-cohomology of arithmetic groups
128
13.3.
Intersection cohomology
129
13.4.
Weighted cohomology
129
CONTENTS xi
13.5.
Continuous cohomology
130
13.6. Applications
of
automorphic
forms to
cohomology 130
13.7.
Construction of cycles and relations to automorphic forms
131
13.8. Hecke
trace formula on the cohomology groups
131
13.9.
Euler
characteristics, Gauss-Bonnet formula
131
13.10.
Cohomology of
S-arithmetic
subgroups
133
13.11.
Boundary cohomology
133
Chapter
14.
if-groups of rings of integers and K-groups of
group rings
135
14.1.
Definitions of algebraic K-groups
135
14.2.
Finite generation of
ЌЏ)
135
14.3.
Relations between
Ю{Ъ)
and cohomology of the
arithmetic groups SL(n, Z)
136
14.4.
Torsion elements of
К{Ђ)
136
14.5.
Applications of
Кг(Ћ Г})
in topology
137
14.6.
Farrell-Jones conjecture,
Borei
conjecture and
Novikov conjecture
137
Chapter
15.
Locally homogeneous manifolds and
period domains
139
15.1.
Homogeneous manifolds as special Riemannian manifolds
139
15.2.
Non-symmetric, but homogeneous spaces
140
15.3.
Hodge structures, period domains and period maps
141
15.4.
Homogeneous, non-Riemannian manifolds
142
15.5.
Clifford-Klein forms of homogeneous spaces
143
15.6.
Space forms: non-Riemannian case
144
15.7.
Counting lattice points on homogeneous varieties
145
Chapter
16.
Non-cofinite discrete groups, geometrically
finite groups
147
16.1.
Geometrically finiteness conditions
147
16.2.
Applications in low dimensional topology
147
16.3.
Spectral theory of geometrically finite groups
149
Chapter
17.
Large scale geometry of discrete groups
151
17.1.
Word metric on discrete groups and growth of groups
151
17.2.
Geometric group theory and property (T)
151
17.3.
Ends of groups
152
17.4.
Ends of locally symmetric spaces and bottom
of the spectrum
154
17.5.
Asymptotic invariants
157
17.6.
L2-invariants
158
17.7.
Boundaries of discrete groups
159
17.8.
Asymptotic geometry of locally symmetric spaces T X
161
CONTENTS
17.9. Isoperimetric
profile,
Dehn
functions of
arithmetic subgroups
162
17.10.
Trees and applications in topology
163
Chapter
18.
Tree lattices
165
18.1.
Structures of tree lattices
165
18.2.
Arithmeticity and density of commensurability groups
of tree lattices
166
18.3.
Rigidity of lattices in products of trees
and CAT(O) groups
167
18.4.
Building lattices and applications to fake
projective
planes
167
Chapter
19.
Hyperbolic groups
169
19.1.
Basic properties of hyperbolic groups
169
19.2.
Rips complex and Gromov boundary
170
Chapter
20.
Mapping class groups and outer automorphism
groups of free groups
173
20.1.
Mapping class groups
173
20.2. Teichmüller
spaces of Riemann surfaces
174
20.3.
Topology of moduli spaces of Riemann surfaces and the
mapping class groups
175
20.4.
Compactifications of
Teichmüller
spaces
176
20.5.
Symmetry of
Teichmüller
spaces
178
Chapter
21.
Outer automorphism group of free groups
and the outer spaces
179
21.1.
Outer automorphism group of free groups
179
21.2.
Outer spaces
179
¿ι.Δ.
Uuter spaces
21.3.
Compactifications of outer spaces
21.4.
Outer automorphism group of non-free groups
180
181
References
183
Index
245
|
| adam_txt |
Contents
Chapter
1.
Introduction
1
Chapter
2.
General comments on references
5
Chapter
3.
Examples of basic arithmetic groups
7
3.1.
Z
as a discrete subgroup of
К
7
3.1.1.
Poisson
summation formula
8
3.1.2.
Riemann
zeta
function
8
3.2.
Z" and lattices in R™
9
3.2.1.
Lattices in R"
10
3.2.2.
Sphere packing
11
3.2.3.
Poisson
summation formula for lattices in R"
12
3.2.4.
Weil-Siegel formula
13
3.2.5.
Voronoi formula
13
3.2.6.
Generalizations of the
Poisson
summation formula
14
3.3.
The modular group
51,(2,
Z)
15
3.3.1.
Fundamental domain of 5L(2,Z) in the upper
half plane
15
3.3.2.
Reduced quadratic forms and reduction theory
16
3.3.3.
Generators of SL(2,Z)
17
3.3.4.
Volume formula for modular curves and locally
symmetric spaces
17
3.3.5.
Moduli space of lattices
17
3.3.6.
Compactifications
18
3.3.7.
Deformation retraction to co-compact subspaces
19
3.3.8.
Geodesic flow, continued fractions and symbolic
dynamics
19
3.3.9.
Congruence subgroups
20
3.3.10.
Dirichlet fundamental domain
21
3.3.11.
Finite generation of discrete groups
22
3.3.12.
Arithmetic Fuchsian groups
23
3.3.13.
Characterization of arithmetic Fuchsian groups
23
3.4.
Spectral theory of
Г\Н
24
3.4.1.
Weyl law
25
3.4.2.
Spectral decomposition
25
3.4.3.
Discrete spectrum and Selberg's ^-conjecture
26
3.4.4.
Selberg trace formula
27
viii CONTENTS
3.4.5.
Generalized Weyl law
28
3.4.6.
Phillips-Sarnak conjecture on cusp Mass forms and
spectral degeneration
28
3.4.7.
Counting lengths of geodesics-the generalized prime
number theorem
29
3.4.8.
Modular symbols
30
3.4.9.
Selberg
zeta
function
31
3.4.10.
Scattering geodesies and generalized
Poisson
relation
32
3.4.11.
Modular forms and Maass forms
33
3.4.12.
Automorphic representations
34
3.4.13.
L-functions
35
3.4.14.
Automorphic forms on
adele
groups
35
3.4.15.
Converse theorems for L-functions
36
3.4.16.
Applications of modular forms
36
Chapter
4.
General arithmetic subgroups and locally
symmetric spaces
37
4.1.
Algebraic groups
37
4.2.
Definition of arithmetic subgroups
38
4.3.
Hubert modular groups
39
4.4.
Congruence subgroups and the congruence kernel
40
4.5.
Arithmetic subgroups as discrete subgroups of Lie groups
41
4.6.
Zariski density of arithmetic subgroups
42
4.7.
Symmetric spaces
43
4.8.
Non-Riemannian symmetric spaces
45
4.9.
Locally symmetric spaces
45
4.10.
Space forms
46
4.11.
Compactness criterion for locally symmetric spaces
47
4.12. Siegel
sets and fundamental sets
48
4.13.
Reduction theory for arithmetic subgroups
49
4.14.
Precise reduction theory for arithmetic subgroups
50
4.15.
Metric properties and Q-rank of locally symmetric spaces
51
4.16.
Volume spectrum of locally symmetric spaces
52
4.17.
Maximal arithmetic subgroups and automorphism groups
53
4.18.
Counting of volumes of hyperbolic manifolds
54
4.19.
Counting of subgroups by index
54
Chapter
5.
Discrete subgroups of Lie groups and arithmeticity of
lattices in Lie groups
57
5.1.
Crystallographic groups and
Auslander
conjecture
57
5.2.
Lattices in
nilpotent
Lie groups and
Margulis
Lemma
58
5.3.
Lattices in solvable Lie groups
60
5.4.
Lattices in
semisimple
Lie groups
61
5.5.
Characterization of arithmetic groups
62
5.6.
Non-arithmeticity of lattices in rank
1
cases
63
CONTENTS ix
5.7. Arithmeticity
of lattices in rank I cases
63
5.8. Linear
discrete subgroups and Tits alternative
64
5.9.
Reflection groups g5
5.10.
Discrete groups related to
Кас-
Moody groups
and algebras
65
5.11.
Infinite dimensional Lie groups and discrete groups
associated with them
66
Chapter
6.
Different completions of
Q
and 5-arithmetic groups over
number fields
69
6.1.
p-adic completions
69
6.2.
5-integers
69
6.3.
5-arithmetic subgroups
70
6.4.
^-arithmetic subgroups as discrete subgroups
of Lie groups
70
Chapter
7.
Global fields and 5-arithmetic groups over function fields
73
7.1.
Function fields
73
7.2.
Global fields
73
7.3.
5-arithmetic subgroups over function fields
74
Chapter
8.
Finiteness properties of arithmetic
and 5-arithmetic groups
75
8.1.
Finite generation
75
8.2.
Bounded generation
76
8.3.
Finite presentations
77
8.4.
Finiteness properties such as FP^o
77
8.5.
Cofinite universal space for proper actions
and arithmetic groups
78
8.6.
Finiteness properties of arithmetic subgroups
79
Chapter
9.
Symmetric spaces, Bruhat-Tits buildings
and their arithmetic quotients
81
9.1.
Flats in symmetric spaces and the spherical Tits building
81
9.2.
Bruhat-Tits buildings
83
9.3.
Action of 5-arithmetic subgroups on products of symmetric
spaces and buildings
83
9.4.
CAT(0)-spaces and CAT(0)-groups
84
9.5.
Reduction theory for 5-arithmetic subgroups
85
Chapter
10.
Compactifications of locally symmetric spaces
87
10.1.
Why locally symmetric spaces are often noncompact
87
10.2.
Compactifications of symmetric spaces
87
10.3.
Limit sets of Kleinian groups and Patterson-Sullivan
theory
89
10.4.
Compactifications of locally symmetric spaces
91
10.5.
Compactifications of Bruhat-Tits buildings
92
x
CONTENTS
10.6. Compactifications
for ^-arithmetic groups
93
10.7.
Geometry and topology of compactifications
94
10.8.
Truncation of locally symmetric spaces
94
Chapter
11.
Rigidity of locally symmetric spaces
97
11.1.
As special Riemannian manifolds
98
11.2.
Local and infinitesimal rigidity of locally
symmetric spaces
98
11.3.
Global (strong) rigidity of locally symmetric spaces
99
11.4.
Super-rigidity of lattices
99
11.5.
Quasi-isometry rigidities of lattices
100
11.6.
Rank rigidity of locally symmetric spaces
102
11.7.
Entropy rigidity of locally symmetric spaces
and simplicial volume
102
11.8.
Rigidity of Hermitian locally symmetric spaces
103
11.9.
Rigidity of pseudo-Riemannian locally symmetric spaces
105
11.10.
Rigidity of non-linear actions of lattices:
Zimmer
program
106
11.11.
Rigidity in
von
Neumann algebras
109
11.12.
Topological rigidity and the
Borei
conjecture 111
11.13.
Methods to prove the rigidities
112
11.14.
Dynamics, flows on locally symmetric spaces
and number theory
113
Chapter
12.
Automorphic forms and automorphic representations
for general arithmetic groups
115
12.1.
Automorphic forms
115
12.2.
Boundary values of eigenfunctions and
automorphic forms
116
12.3.
Spectral decomposition
117
12.4.
Weyl law
118
12.5.
Counting of eigenvalues for a tower of spaces
118
12.6.
Quantum chaos
119
12.7.
Arthur-Selberg trace formula
120
12.8.
Selberg
zeta
function
121
12.9.
Counting of lengths of geodesies and volumes of tori
122
12.10.
L-functions of automorphic representations
122
12.11.
Meromorphic continuation of
Eisenstein
series
123
12.12.
Constant term of
Eisenstein
series
124
12.13. Langlands
program
124
12.14.
Spectral theory over function fields: an example
125
Chapter
13.
Cohomology of arithmetic groups
127
13.1.
Cohomology groups
127
13.2.
L2- and ^-cohomology of arithmetic groups
128
13.3.
Intersection cohomology
129
13.4.
Weighted cohomology
129
CONTENTS xi
13.5.
Continuous cohomology
130
13.6. Applications
of
automorphic
forms to
cohomology 130
13.7.
Construction of cycles and relations to automorphic forms
131
13.8. Hecke
trace formula on the cohomology groups
131
13.9.
Euler
characteristics, Gauss-Bonnet formula
131
13.10.
Cohomology of
S-arithmetic
subgroups
133
13.11.
Boundary cohomology
133
Chapter
14.
if-groups of rings of integers and K-groups of
group rings
135
14.1.
Definitions of algebraic K-groups
135
14.2.
Finite generation of
ЌЏ)
135
14.3.
Relations between
Ю{Ъ)
and cohomology of the
arithmetic groups SL(n, Z)
136
14.4.
Torsion elements of
К{Ђ)
136
14.5.
Applications of
Кг(Ћ\Г})
in topology
137
14.6.
Farrell-Jones conjecture,
Borei
conjecture and
Novikov conjecture
137
Chapter
15.
Locally homogeneous manifolds and
period domains
139
15.1.
Homogeneous manifolds as special Riemannian manifolds
139
15.2.
Non-symmetric, but homogeneous spaces
140
15.3.
Hodge structures, period domains and period maps
141
15.4.
Homogeneous, non-Riemannian manifolds
142
15.5.
Clifford-Klein forms of homogeneous spaces
143
15.6.
Space forms: non-Riemannian case
144
15.7.
Counting lattice points on homogeneous varieties
145
Chapter
16.
Non-cofinite discrete groups, geometrically
finite groups
147
16.1.
Geometrically finiteness conditions
147
16.2.
Applications in low dimensional topology
147
16.3.
Spectral theory of geometrically finite groups
149
Chapter
17.
Large scale geometry of discrete groups
151
17.1.
Word metric on discrete groups and growth of groups
151
17.2.
Geometric group theory and property (T)
151
17.3.
Ends of groups
152
17.4.
Ends of locally symmetric spaces and bottom
of the spectrum
154
17.5.
Asymptotic invariants
157
17.6.
L2-invariants
158
17.7.
Boundaries of discrete groups
159
17.8.
Asymptotic geometry of locally symmetric spaces T\X
161
CONTENTS
17.9. Isoperimetric
profile,
Dehn
functions of
arithmetic subgroups
162
17.10.
Trees and applications in topology
163
Chapter
18.
Tree lattices
165
18.1.
Structures of tree lattices
165
18.2.
Arithmeticity and density of commensurability groups
of tree lattices
166
18.3.
Rigidity of lattices in products of trees
and CAT(O) groups
167
18.4.
Building lattices and applications to fake
projective
planes
167
Chapter
19.
Hyperbolic groups
169
19.1.
Basic properties of hyperbolic groups
169
19.2.
Rips complex and Gromov boundary
170
Chapter
20.
Mapping class groups and outer automorphism
groups of free groups
173
20.1.
Mapping class groups
173
20.2. Teichmüller
spaces of Riemann surfaces
174
20.3.
Topology of moduli spaces of Riemann surfaces and the
mapping class groups
175
20.4.
Compactifications of
Teichmüller
spaces
176
20.5.
Symmetry of
Teichmüller
spaces
178
Chapter
21.
Outer automorphism group of free groups
and the outer spaces
179
21.1.
Outer automorphism group of free groups
179
21.2.
Outer spaces
179
¿ι.Δ.
Uuter spaces
21.3.
Compactifications of outer spaces
21.4.
Outer automorphism group of non-free groups
180
181
References
183
Index
245 |
| any_adam_object | 1 |
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| author | Ji, Lizhen 1964- |
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| ctrlnum | (OCoLC)212909009 (DE-599)HBZHT015644992 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV035052409 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:57:07Z |
| indexdate | 2024-07-09T21:21:06Z |
| institution | BVB |
| isbn | 9780821846759 0821846752 9780821848661 |
| language | English |
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| publisher | American Mathematical Society International Press |
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| series | AMS/IP studies in advanced mathematics |
| series2 | AMS/IP studies in advanced mathematics |
| spelling | Ji, Lizhen 1964- Verfasser (DE-588)120496348 aut Arithmetic groups and their generalizations what, why, and how Lizhen Ji Providence, R.I. American Mathematical Society 2008 [Somerville, MA] International Press XVII, 259 S. Ill. txt rdacontent n rdamedia nc rdacarrier AMS/IP studies in advanced mathematics 43 Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. 183-243) and index Arithmetic groups Linear algebraic groups Arithmetische Gruppe (DE-588)4255663-6 gnd rswk-swf Arithmetische Gruppe (DE-588)4255663-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3833-3 AMS/IP studies in advanced mathematics 43 (DE-604)BV011103148 43 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016721056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ji, Lizhen 1964- Arithmetic groups and their generalizations what, why, and how AMS/IP studies in advanced mathematics Arithmetic groups Linear algebraic groups Arithmetische Gruppe (DE-588)4255663-6 gnd |
| subject_GND | (DE-588)4255663-6 |
| title | Arithmetic groups and their generalizations what, why, and how |
| title_auth | Arithmetic groups and their generalizations what, why, and how |
| title_exact_search | Arithmetic groups and their generalizations what, why, and how |
| title_exact_search_txtP | Arithmetic groups and their generalizations what, why, and how |
| title_full | Arithmetic groups and their generalizations what, why, and how Lizhen Ji |
| title_fullStr | Arithmetic groups and their generalizations what, why, and how Lizhen Ji |
| title_full_unstemmed | Arithmetic groups and their generalizations what, why, and how Lizhen Ji |
| title_short | Arithmetic groups and their generalizations |
| title_sort | arithmetic groups and their generalizations what why and how |
| title_sub | what, why, and how |
| topic | Arithmetic groups Linear algebraic groups Arithmetische Gruppe (DE-588)4255663-6 gnd |
| topic_facet | Arithmetic groups Linear algebraic groups Arithmetische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016721056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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