Systolic geometry and topology:
The systole of a compact metric space
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2007]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 137 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Zusammenfassung: | The systole of a compact metric space |
| Beschreibung: | xiv, 222 Seiten |
| ISBN: | 9780821841778 0821841777 |
Internformat
MARC
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| 100 | 1 | |a Katz, Mikhail Gersh |d 1958- |e Verfasser |0 (DE-588)124044840 |4 aut | |
| 245 | 1 | 0 | |a Systolic geometry and topology |c Mikhail G. Katz. With an appendix by Jake P. Solomon |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2007] | |
| 264 | 4 | |c © 2007 | |
| 300 | |a xiv, 222 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 137 | |
| 520 | 3 | |a The systole of a compact metric space | |
| 650 | 7 | |a Geometria diferencial (textos avançados) |2 larpcal | |
| 650 | 7 | |a Geometria global |2 larpcal | |
| 650 | 4 | |a Géométrie algébrique | |
| 650 | 4 | |a Inégalités (Mathématiques) | |
| 650 | 4 | |a Riemann, Surfaces de | |
| 650 | 7 | |a Topologia |2 larpcal | |
| 650 | 4 | |a Topologie | |
| 650 | 7 | |a Variedades riemannianas |2 larpcal | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Inequalities (Mathematics) | |
| 650 | 4 | |a Riemann surfaces | |
| 650 | 4 | |a Topology | |
| 650 | 0 | 7 | |a Geometrische Invariantentheorie |0 (DE-588)4156712-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riemannsche Fläche |0 (DE-588)4049991-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Solomon, Jake P. |0 (DE-588)1178700291 |4 wat | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1364-4 |
| 830 | 0 | |a Mathematical surveys and monographs |v Volume 137 |w (DE-604)BV000018014 |9 137 | |
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Datensatz im Suchindex
| _version_ | 1804136556521324544 |
|---|---|
| adam_text | Contents
Preface
xi
Acknowledgments
xiii
Part
1.
Systolic geometry in dimension
2 1
Chapter
1.
Geometry and topology of systoles
3
1.1.
From Loewner to Gromov via
Berger
3
1.2.
Contents of Part
1 6
1.3.
Contents of Part
2 7
Chapter
2.
Historical remarks
13
2.1.
A la recherche
des
systoles, by Marcel
Berger
13
2.2.
Charles Loewner
(1893-1968) 14
2.3.
Pu, Pao
Ming
(1910-1988) 19
2.4.
A note to the reader
19
Chapter
3.
The
theorema
egregium of Gauss
21
3.1.
Intrinsic vs extrinsic properties
21
3.2.
Preliminaries to the
theorema
egregium
22
3.3.
The
theorema
egregium of Gauss
24
3.4.
The Laplacian formula for Gaussian curvature
25
Chapter
4.
Global geometry of surfaces
29
4.1.
Metric preliminaries
29
4.2.
Geodesic equation and closed geodesies
32
4.3.
Surfaces of constant curvature
33
4.4.
Flat surfaces
35
4.5.
Hyperbolic surfaces
35
4.6.
Topological preliminaries
37
Chapter
5.
Inequalities of Loewner and
Pu
39
5.1.
Definition of systole
39
5.2.
Isoperimetric inequality and Pu s inequality
39
5.3.
Hermite and
Bergé-Martinet
constants
41
5.4.
The Loewner inequality
42
Chapter
6.
Systolic applications of integral geometry
43
6.1.
An integral-geometric identity
43
6.2.
Two proofs of the Loewner inequality
44
6.3. Hopf
fibration and the Hamilton quaternions
46
viii CONTENTS
6.4.
Double fibration of 5O(3) and integral geometry on S2
46
6.5.
Proof of Pu s inequality
48
6.6.
A, table of optimal systolic ratios of surfaces
48
Chapter
7.
A primer on surfaces
51
7.1.
Hyperelliptic involution
51
7.2.
Hyperelliptic surfaces
52
7.3.
Ovalless surfaces
53
7.4.
Katok s entropy inequality
54
Chapter
8.
Filling area theorem for hyperelliptic surfaces
57
8.1.
To fill a circle: an introduction
57
8.2.
Relative Pu s way
59
8.3.
Outline of proof of optimal displacement bound
60
8.4.
Near optimal surfaces and the football
61
8.5.
Finding a short figure eight geodesic
63
8.6.
Proof of circle filling: Step
1 63
8.7.
Proof of circle filling: Step
2 64
Chapter
9,
Hyperelliptic surfaces are Loewner
69
9.1.
Hermite constant and Loewner surfaces
69
9.2.
Basic estimates
70
9.3.
Hyperelliptic surfaces and ^-regularity
70
9.4.
Proof of the genus two Loewner bound
71
Chapter
10.
An optimal inequality for CAT(O) metrics
75
10.1.
Hyperelliptic surfaces of
nonpositive
curvature
75
10.2.
Distinguishing
16
points on the Bolza surface
76
10.3.
A flat, singular metric in genus two
77
10.4.
Voronoi cells and
Euler
characteristic
80
10.5.
Arbitrary metrics on the Bolza surface
82
Chapter
11.
Volume entropy and asymptotic upper bounds
85
11.1.
Entropy and systole
85
11.2.
Basic estimate
86
11.3.
Asymptotic behavior of systolic ratio for large genus
88
11.4.
When is a surface Loewner?
89
Part
2.
Systolic geometry and topology in
η
dimensions
91
Chapter
12.
Systoles and their category
93
12.1.
Systoles
93
12.2.
Gromov s spectacular inequality for the 1-systole
95
12.3.
Systolic category
97
12.4.
Some examples and questions
99
12.5.
Essentialness and Lusternik-Schnirelmann category
100
12.6.
Inessential manifolds and pullback metrics
101
12.7.
Manifolds of dimension
3 102
12.8.
Category of simply connected manifolds
104
Chapter
13.
Gromov s optimal stable systolic, inequality for CPn
107
CONTENTS
ix
13.1.
Federer s proof of the
Wirtinger
inequality
107
13.2.
Optimal inequality for complex
projective
space
108
13.3.
Quaternionic
projective
plane
110
Chapter
14.
Systolic inequalities dependent on Massey products
113
14.1.
Massey Products via Differential Graded Associative Algebras
113
14.2.
Integrality of
de Rham
Massey products
115
14.3.
Gromov s calculation in the presence of a Massey
116
14.4.
A homogeneous example
118
Chapter
15.
Cup products and stable systoles
119
15.1.
Introduction
119
15.2.
Statement of main results
120
15.3.
Results for the
conformai
systole
122
15.4.
Some topological preliminaries
124
15.5.
Ring structure-dependent bound via Banaszczyk
125
15.6.
Inequalities based on cap products,
Poincaré
duality
127
15.7.
A sharp inequality in codimension
1 129
15.8.
A conformally invariant inequality in middle dimension
130
15.9.
A pair of
conformai
systoles
130
15.10.
A sublinear
estimate for a single systole
133
Chapter
16.
Dual-critical lattices and systoles
135
16.1.
Introduction
135
16.2.
Statement of main theorems
135
16.3.
Norms on
(co-)homology
137
16.4.
Definition of
conformai
systoles
138
16.5.
Jacobi variety and Abel-Jacobi map
139
16.6.
Summary of the proofs
140
16.7.
Harmonic one-forms of constant norm and flat tori
141
16.8.
Norm duality and the cup product
144
16.9.
Holder inequality in cohomology and case of equality
146
16.10.
Proof of optimal
(1,
η
-
l)-inequality
147
16.11.
Consequences of equality, criterion of duabperfection
148
16.12.
Characterisation of equality in (l,n
—
l)-inequality
149
16.13.
Construction of all extremal metrics
151
16.14.
Submersions onto tori
152
Chapter
17.
Generalized degree and Loewner-type inequalities
155
17.1.
Burago-Ivanov-Gromov inequality
155
17.2.
Generalized degree and BIG(n, b) inequality
156
17.3.
Pu s inequality and generalisations
157
17.4.
A Pu
times Loewner inequality
158
17.5.
A decomposition of the John ellipsoid
159
17.6.
An area-nonexpanding map
159
17.7.
Proof of BIG(n, b)-inequality and Theorem
17.4.1 161
Chapter
18.
Higher inequalities of Loewner-Gromov type
163
18.1.
Introduction, conjectures, and some results
163
18.2.
Notion of degree when dimension exceeds
Betti
number
164
x
CONTENTS
18.3.
Conformai
BIG(n.p)-inequalit.y 166
18.4.
Stable
norms and
conformai
norms
168
18.5.
Existence of £-p-minimizers in cohomology classes
169
18.6.
Existence of harmonic forms with constant norm
171
18.7.
The BI construction adapted to
conformai
norms
173
18.8.
Abel-Jacobi map for
conformai
norms
174
18.9.
Attaining the
conformai
BIG bound
174
Chapter
19.
Systolic inequalities for Lp norms
177
19.1.
Case
η
>
b
and V norms in homology
177
19.2.
The BI construction in the case
n
>
h
178
19.3.
Proof of bound on orthogonal Jacobian
> 178
19.4.
Attaining the
conformai BIG(n,ò)
bound
180
Chapter
20.
Four-manifold systole asymptotics
181
20.1.
Schottky problem and the surjectivity conjecture
181
20.2.
Conway-Thompson lattices CT?i and idea of proof
183
20.3.
Norms in cohomology
183
20.4.
Conformai
length and systolic flavors
184
20.5.
Systoles of definite intersection forms
185
20.6.
Buser-Sarnak theorem
186
20.7.
Sign reversal procedure SR and
Aut
(ƒ.„,
^-invariance
186
20.8.
Lorentz
construction of Leech lattice and line CT^
187
20.9.
Three quadratic forms in the plane
189
20.10.
Replacing
λ]
by the geometric mean
(Αιλ2)1/2
190
20.11.
Period map and proof of main theorem
192
Appendix A. Period map image density (by Jake Solomon)
195
A.I. Introduction and outline of proof
195
A.
2.
Symplectic forms and the self-dual line
196
A.3. A lemma from hyperbolic geometry
197
A.
4.
Diffeomorphism group of blow-up of
projective
plane
198
A.
5.
Background material from symplectic geometry
199
A.
6.
Proof of density of image of period map
201
Appendix B. Open problems
205
B.I. Topology
205
B.2. Geometry
206
B.3. Arithmetic
206
Bibliography
209
Index
221
|
| adam_txt |
Contents
Preface
xi
Acknowledgments
xiii
Part
1.
Systolic geometry in dimension
2 1
Chapter
1.
Geometry and topology of systoles
3
1.1.
From Loewner to Gromov via
Berger
3
1.2.
Contents of Part
1 6
1.3.
Contents of Part
2 7
Chapter
2.
Historical remarks
13
2.1.
A la recherche
des
systoles, by Marcel
Berger
13
2.2.
Charles Loewner
(1893-1968) 14
2.3.
Pu, Pao
Ming
(1910-1988) 19
2.4.
A note to the reader
19
Chapter
3.
The
theorema
egregium of Gauss
21
3.1.
Intrinsic vs extrinsic properties
21
3.2.
Preliminaries to the
theorema
egregium
22
3.3.
The
theorema
egregium of Gauss
24
3.4.
The Laplacian formula for Gaussian curvature
25
Chapter
4.
Global geometry of surfaces
29
4.1.
Metric preliminaries
29
4.2.
Geodesic equation and closed geodesies
32
4.3.
Surfaces of constant curvature
33
4.4.
Flat surfaces
35
4.5.
Hyperbolic surfaces
35
4.6.
Topological preliminaries
37
Chapter
5.
Inequalities of Loewner and
Pu
39
5.1.
Definition of systole
39
5.2.
Isoperimetric inequality and Pu's inequality
39
5.3.
Hermite and
Bergé-Martinet
constants
41
5.4.
The Loewner inequality
42
Chapter
6.
Systolic applications of integral geometry
43
6.1.
An integral-geometric identity
43
6.2.
Two proofs of the Loewner inequality
44
6.3. Hopf
fibration and the Hamilton quaternions
46
viii CONTENTS
6.4.
Double fibration of 5O(3) and integral geometry on S2
46
6.5.
Proof of Pu's inequality
48
6.6.
A, table of optimal systolic ratios of surfaces
48
Chapter
7.
A primer on surfaces
51
7.1.
Hyperelliptic involution
51
7.2.
Hyperelliptic surfaces
52
7.3.
Ovalless surfaces
53
7.4.
Katok's entropy inequality
54
Chapter
8.
Filling area theorem for hyperelliptic surfaces
57
8.1.
To fill a circle: an introduction
57
8.2.
Relative Pu's way
59
8.3.
Outline of proof of optimal displacement bound
60
8.4.
Near optimal surfaces and the football
61
8.5.
Finding a short figure eight geodesic
63
8.6.
Proof of circle filling: Step
1 63
8.7.
Proof of circle filling: Step
2 64
Chapter
9,
Hyperelliptic surfaces are Loewner
69
9.1.
Hermite constant and Loewner surfaces
69
9.2.
Basic estimates
70
9.3.
Hyperelliptic surfaces and ^-regularity
70
9.4.
Proof of the genus two Loewner bound
71
Chapter
10.
An optimal inequality for CAT(O) metrics
75
10.1.
Hyperelliptic surfaces of
nonpositive
curvature
75
10.2.
Distinguishing
16
points on the Bolza surface
76
10.3.
A flat, singular metric in genus two
77
10.4.
Voronoi cells and
Euler
characteristic
80
10.5.
Arbitrary metrics on the Bolza surface
82
Chapter
11.
Volume entropy and asymptotic upper bounds
85
11.1.
Entropy and systole
85
11.2.
Basic estimate
86
11.3.
Asymptotic behavior of systolic ratio for large genus
88
11.4.
When is a surface Loewner?
89
Part
2.
Systolic geometry and topology in
η
dimensions
91
Chapter
12.
Systoles and their category
93
12.1.
Systoles
93
12.2.
Gromov's spectacular inequality for the 1-systole
95
12.3.
Systolic category
97
12.4.
Some examples and questions
99
12.5.
Essentialness and Lusternik-Schnirelmann category
100
12.6.
Inessential manifolds and pullback metrics
101
12.7.
Manifolds of dimension
3 102
12.8.
Category of simply connected manifolds
104
Chapter
13.
Gromov's optimal stable systolic, inequality for CPn
107
CONTENTS
ix
13.1.
Federer's proof of the
Wirtinger
inequality
107
13.2.
Optimal inequality for complex
projective
space
108
13.3.
Quaternionic
projective
plane
110
Chapter
14.
Systolic inequalities dependent on Massey products
113
14.1.
Massey Products via Differential Graded Associative Algebras
113
14.2.
Integrality of
de Rham
Massey products
115
14.3.
Gromov's calculation in the presence of a Massey
116
14.4.
A homogeneous example
118
Chapter
15.
Cup products and stable systoles
119
15.1.
Introduction
119
15.2.
Statement of main results
120
15.3.
Results for the
conformai
systole
122
15.4.
Some topological preliminaries
124
15.5.
Ring structure-dependent bound via Banaszczyk
125
15.6.
Inequalities based on cap products,
Poincaré
duality
127
15.7.
A sharp inequality in codimension
1 129
15.8.
A conformally invariant inequality in middle dimension
130
15.9.
A pair of
conformai
systoles
130
15.10.
A sublinear
estimate for a single systole
133
Chapter
16.
Dual-critical lattices and systoles
135
16.1.
Introduction
135
16.2.
Statement of main theorems
135
16.3.
Norms on
(co-)homology
137
16.4.
Definition of
conformai
systoles
138
16.5.
Jacobi variety and Abel-Jacobi map
139
16.6.
Summary of the proofs
140
16.7.
Harmonic one-forms of constant norm and flat tori
141
16.8.
Norm duality and the cup product
144
16.9.
Holder inequality in cohomology and case of equality
146
16.10.
Proof of optimal
(1,
η
-
l)-inequality
147
16.11.
Consequences of equality, criterion of duabperfection
148
16.12.
Characterisation of equality in (l,n
—
l)-inequality
149
16.13.
Construction of all extremal metrics
151
16.14.
Submersions onto tori
152
Chapter
17.
Generalized degree and Loewner-type inequalities
155
17.1.
Burago-Ivanov-Gromov inequality
155
17.2.
Generalized degree and BIG(n, b) inequality
156
17.3.
Pu's inequality and generalisations
157
17.4.
A Pu
times Loewner inequality
158
17.5.
A decomposition of the John ellipsoid
159
17.6.
An area-nonexpanding map
159
17.7.
Proof of BIG(n, b)-inequality and Theorem
17.4.1 161
Chapter
18.
Higher inequalities of Loewner-Gromov type
163
18.1.
Introduction, conjectures, and some results
163
18.2.
Notion of degree when dimension exceeds
Betti
number
164
x
CONTENTS
18.3.
Conformai
BIG(n.p)-inequalit.y 166
18.4.
Stable
norms and
conformai
norms
168
18.5.
Existence of £-p-minimizers in cohomology classes
169
18.6.
Existence of harmonic forms with constant norm
171
18.7.
The BI construction adapted to
conformai
norms
173
18.8.
Abel-Jacobi map for
conformai
norms
174
18.9.
Attaining the
conformai
BIG bound
174
Chapter
19.
Systolic inequalities for Lp norms
177
19.1.
Case
η
>
b
and V norms in homology
177
19.2.
The BI construction in the case
n
>
h
178
19.3.
Proof of bound on orthogonal Jacobian
> 178
19.4.
Attaining the
conformai BIG(n,ò)
bound
180
Chapter
20.
Four-manifold systole asymptotics
181
20.1.
Schottky problem and the surjectivity conjecture
181
20.2.
Conway-Thompson lattices CT?i and idea of proof
183
20.3.
Norms in cohomology
183
20.4.
Conformai
length and systolic flavors
184
20.5.
Systoles of definite intersection forms
185
20.6.
Buser-Sarnak theorem
186
20.7.
Sign reversal procedure SR and
Aut
(ƒ.„,
^-invariance
186
20.8.
Lorentz
construction of Leech lattice and line CT^
187
20.9.
Three quadratic forms in the plane
189
20.10.
Replacing
λ]
by the geometric mean
(Αιλ2)1/2
190
20.11.
Period map and proof of main theorem
192
Appendix A. Period map image density (by Jake Solomon)
195
A.I. Introduction and outline of proof
195
A.
2.
Symplectic forms and the self-dual line
196
A.3. A lemma from hyperbolic geometry
197
A.
4.
Diffeomorphism group of blow-up of
projective
plane
198
A.
5.
Background material from symplectic geometry
199
A.
6.
Proof of density of image of period map
201
Appendix B. Open problems
205
B.I. Topology
205
B.2. Geometry
206
B.3. Arithmetic
206
Bibliography
209
Index
221 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Katz, Mikhail Gersh 1958- |
| author_GND | (DE-588)124044840 (DE-588)1178700291 |
| author_facet | Katz, Mikhail Gersh 1958- |
| author_role | aut |
| author_sort | Katz, Mikhail Gersh 1958- |
| author_variant | m g k mg mgk |
| building | Verbundindex |
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| callnumber-search | QA564 |
| callnumber-sort | QA 3564 |
| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)77716978 (DE-599)BVBBV022469779 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV022469779 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:44:07Z |
| indexdate | 2024-07-09T20:58:17Z |
| institution | BVB |
| isbn | 9780821841778 0821841777 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015677289 |
| oclc_num | 77716978 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-384 DE-634 DE-11 DE-355 DE-BY-UBR DE-29T |
| owner_facet | DE-19 DE-BY-UBM DE-384 DE-634 DE-11 DE-355 DE-BY-UBR DE-29T |
| physical | xiv, 222 Seiten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Katz, Mikhail Gersh 1958- Verfasser (DE-588)124044840 aut Systolic geometry and topology Mikhail G. Katz. With an appendix by Jake P. Solomon Providence, Rhode Island American Mathematical Society [2007] © 2007 xiv, 222 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 137 The systole of a compact metric space Geometria diferencial (textos avançados) larpcal Geometria global larpcal Géométrie algébrique Inégalités (Mathématiques) Riemann, Surfaces de Topologia larpcal Topologie Variedades riemannianas larpcal Geometry, Algebraic Inequalities (Mathematics) Riemann surfaces Topology Geometrische Invariantentheorie (DE-588)4156712-2 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s Riemannsche Fläche (DE-588)4049991-1 s Geometrische Invariantentheorie (DE-588)4156712-2 s DE-604 Solomon, Jake P. (DE-588)1178700291 wat Erscheint auch als Online-Ausgabe 978-1-4704-1364-4 Mathematical surveys and monographs Volume 137 (DE-604)BV000018014 137 http://www.gbv.de/dms/goettingen/522828477.pdf Inhaltsverzeichnis Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Katz, Mikhail Gersh 1958- Systolic geometry and topology Mathematical surveys and monographs Geometria diferencial (textos avançados) larpcal Geometria global larpcal Géométrie algébrique Inégalités (Mathématiques) Riemann, Surfaces de Topologia larpcal Topologie Variedades riemannianas larpcal Geometry, Algebraic Inequalities (Mathematics) Riemann surfaces Topology Geometrische Invariantentheorie (DE-588)4156712-2 gnd Riemannsche Fläche (DE-588)4049991-1 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| subject_GND | (DE-588)4156712-2 (DE-588)4049991-1 (DE-588)4185712-4 |
| title | Systolic geometry and topology |
| title_auth | Systolic geometry and topology |
| title_exact_search | Systolic geometry and topology |
| title_exact_search_txtP | Systolic geometry and topology |
| title_full | Systolic geometry and topology Mikhail G. Katz. With an appendix by Jake P. Solomon |
| title_fullStr | Systolic geometry and topology Mikhail G. Katz. With an appendix by Jake P. Solomon |
| title_full_unstemmed | Systolic geometry and topology Mikhail G. Katz. With an appendix by Jake P. Solomon |
| title_short | Systolic geometry and topology |
| title_sort | systolic geometry and topology |
| topic | Geometria diferencial (textos avançados) larpcal Geometria global larpcal Géométrie algébrique Inégalités (Mathématiques) Riemann, Surfaces de Topologia larpcal Topologie Variedades riemannianas larpcal Geometry, Algebraic Inequalities (Mathematics) Riemann surfaces Topology Geometrische Invariantentheorie (DE-588)4156712-2 gnd Riemannsche Fläche (DE-588)4049991-1 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| topic_facet | Geometria diferencial (textos avançados) Geometria global Géométrie algébrique Inégalités (Mathématiques) Riemann, Surfaces de Topologia Topologie Variedades riemannianas Geometry, Algebraic Inequalities (Mathematics) Riemann surfaces Topology Geometrische Invariantentheorie Riemannsche Fläche Topologische Mannigfaltigkeit |
| url | http://www.gbv.de/dms/goettingen/522828477.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT katzmikhailgersh systolicgeometryandtopology AT solomonjakep systolicgeometryandtopology |
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Inhaltsverzeichnis