Compactifications of symmetric and locally symmetric spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2006
|
| Series: | Mathematics: theory and applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 479 S. |
| ISBN: | 0817632476 9780817632472 |
Staff View
MARC
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| 245 | 1 | 0 | |a Compactifications of symmetric and locally symmetric spaces |c Armand Borel ; Lizhen Ji |
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Mathematics: theory and applications | |
| 650 | 4 | |a Kompaktifizierung - Lokal symmetrischer Raum | |
| 650 | 4 | |a Kompaktifizierung - Symmetrischer Raum | |
| 650 | 4 | |a Compactifications | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
..................................................... ix
0
Introduction
................................................. 1
0.1
History of compactifications
.................................
2
0.2
New points of view in this book
.............................. 14
0.3
Organization and outline of the book
.......................... 16
0.4
Topics related to the book but not covered and classification of
references
................................................. 17
Part I
Compactìfications
of Riemannian Symmetric Spaces
1
Review of Classical
Compactìfications
of Symmetric Spaces
......... 27
1.1 Real parabolic subgroups
.................................... 28
1.2
Geodesic compactification and Tits bunding
.................... 39
1.3
Karpelevič
compactification
.................................. 50
1.4
Satake
compactìfications
.................................... 55
1.5
Baily-Borel compactification
................................. 77
1.6
Furstenberg
compactìfications................................
91
1.7
Martin
compactìfications....................................
97
2
Uniform Construction of
Compactìfications
of Symmetric Spaces
___ 107
1.8
Formulation of the uniform construction
....................... 108
1.9 Siegel
sets and generalizations
................................ 114
1.10
Uniform construction of the maximal Satake compactification
..... 123
1.11
Uniform construction of
nonmaximal
Satake compactifications
___ 129
1.12
Uniform construction of the geodesic compactification
........... 139
1.13
Uniform construction of the Martin compactification
............. 144
1.14
Uniform construction of the
Karpelevič
compactification
......... 149
1.15
Real
Borei-Serre
partial compactification
...................... 159
viii Contents
3
Properties of Compactifications of Symmetric Spaces
.............. 165
1.16
Relations between the compactifications
....................... 165
1.17
More constructions of the maximal Satake compactification
....... 168
1.18
Compactifications as a topological ball
......................... 174
1.19
Dual-cell compactification and maximal Satake compactification
as a manifold with corners
................................... 182
Part
Π
Smooth Compactifications of
Semisimple
Symmetric Spaces
4
Smooth Compactifications of Riemannian Symmetric Spaces G/K
... 203
Π.1
Gluing of manifolds with corners
............................. 204
Π.2
The Oshima compactification of G/K
......................... 210
5 Semisimple
Symmetric Spaces G/H
.............................215
Π.3
Generalities on
semisimple
symmetric spaces
................... 215
Π.4
Some real forms He of
Η
.................................... 217
6
The Real Points of Complex Symmetric Spaces Defined over
Ж
......221
П.5
Galois Cohomology
........................................ 221
П.6
Orbits of
G
in (G/HXE)
.................................... 224
П.7
Examples
................................................. 230
7
The DeConcini-Procesi Compactification of a Complex Symmetric
Space and Its Real Points
......................................233
П.8
Generalities on
semisimple
symmetric spaces
................... 233
П.9
The DeConcini-Procesi wonderful compactification of G/H
...... 236
П.10
Real points of G/H
......................................... 239
П.11
A characterization of the involutions
σε
........................ 244
8
The Oshima-Sekiguchi Compactification of G/K and Comparison
wi<hG/HW(R)
...............................................249
П.
12
Preliminaries on
semisimple
symmetric spaces
.................. 249
П.13
The Oshima-Sekiguchi compactification of G/K
................ 253
П.14
Comparison with G/HW(E)
................................. 257
Part
Ш
Compactifications of Locally Symmetric Spaces
9
Classical Compactifications of Locally Symmetric Spaces
...........267
Ш.1
Rational parabolic subgroups
................................. 268
Ш.2
Arithmetic subgroups and reduction theories
.................... 277
Ш.З
Satake compactifications of locally symmetric spaces
............ 286
Ш.4
Baily-Borel compactification
................................. 293
Ш.5
Borei-Serre
compactification
................................. 301
Contents ix
Ш.6
Reductive
Borei-Serre compactification
........................ 309
Ш.7
Toroidal compactifications
................................... 314
10
Uniform Construction of Compactifications of Locally Symmetric
Spaces
......................................................323
Ш.8
Formulation of the uniform construction
....................... 324
Ш.9
Uniform construction of the
Borei-Serre
compactification
........ 326
ШЛО
Uniform construction of the reductive
Borei-Serre
compactification
338
Ш.
11
Uniform construction of the maximal Satake compactification
.... 345
Ш.12
Tits compactification
....................................... 350
Ш.13
Borei-Serre
compactification of homogeneous spaces F G
...... 355
III.
14
Reductive
Borei-Serre
compactification of homogeneous spaces
r G
.................................................... 359
11
Properties of Compactifications of Locally Symmetric Spaces
.......365
Ш.15
Relations between the compactifications
...................... 366
Ш.16
Self-gluing of
Borei-Serre
compactification into
Borel-Serre-Oshima compactification
........................ 370
12
Subgroup Compactifications of T G
............................375
Ш.17
Maximal discrete subgroups and space of subgroups
............ 376
Ш.18
Subgroup compactification of V G and
Г Х
.................. 382
Ш.19
Spaces of flags in Rn, flag lattices, and compactifications of
SL(n, Z) SL(n, E)
........................................ 386
13
Metric Properties of Compactifications of Locally
Symmetric Spaces
Г Х
.......................................399
Ш.20
Eventually distance-minimizing geodesies and geodesic
compactification of F X
................................... 400
Ш.21
Rough geometry of
Г Х
and
Siegel
conjecture on metrics on
Siegel
sets
............................................... 405
Ш.22
Hyperbolic compactifications and extension of holomorphic maps
from the punctured disk to Hermitian locally symmetric spaces
... 409
Ш.23
Continuous spectrum, boundaries of compactifications, and
scattering geodesies of
Г Х
................................ 416
References
......................................................423
Notation Index
...................................................451
Index
...........................................................459
|
| any_adam_object | 1 |
| author | Borel, Armand 1923-2003 Ji, Lizhen 1964- |
| author_GND | (DE-588)119089106 (DE-588)120496348 |
| author_facet | Borel, Armand 1923-2003 Ji, Lizhen 1964- |
| author_role | aut aut |
| author_sort | Borel, Armand 1923-2003 |
| author_variant | a b ab l j lj |
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| bvnumber | BV019872135 |
| callnumber-first | Q - Science |
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| callnumber-search | QA611.23 |
| callnumber-sort | QA 3611.23 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 |
| ctrlnum | (OCoLC)254814195 (DE-599)BVBBV019872135 |
| dewey-full | 516.362 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.362 |
| dewey-search | 516.362 |
| dewey-sort | 3516.362 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019872135 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:08:04Z |
| institution | BVB |
| isbn | 0817632476 9780817632472 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013196407 |
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| physical | XIII, 479 S. |
| publishDate | 2006 |
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| publisher | Birkhäuser |
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| series2 | Mathematics: theory and applications |
| spelling | Borel, Armand 1923-2003 Verfasser (DE-588)119089106 aut Compactifications of symmetric and locally symmetric spaces Armand Borel ; Lizhen Ji Boston [u.a.] Birkhäuser 2006 XIII, 479 S. txt rdacontent n rdamedia nc rdacarrier Mathematics: theory and applications Kompaktifizierung - Lokal symmetrischer Raum Kompaktifizierung - Symmetrischer Raum Compactifications Symmetric spaces Lokal symmetrischer Raum (DE-588)4168100-9 gnd rswk-swf Kompaktifizierung (DE-588)4164859-6 gnd rswk-swf Symmetrischer Raum (DE-588)4184206-6 gnd rswk-swf Kompaktifizierung (DE-588)4164859-6 s Symmetrischer Raum (DE-588)4184206-6 s Lokal symmetrischer Raum (DE-588)4168100-9 s b DE-604 Ji, Lizhen 1964- Verfasser (DE-588)120496348 aut Erscheint auch als Online-Ausgabe 0-8176-4466-0 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013196407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borel, Armand 1923-2003 Ji, Lizhen 1964- Compactifications of symmetric and locally symmetric spaces Kompaktifizierung - Lokal symmetrischer Raum Kompaktifizierung - Symmetrischer Raum Compactifications Symmetric spaces Lokal symmetrischer Raum (DE-588)4168100-9 gnd Kompaktifizierung (DE-588)4164859-6 gnd Symmetrischer Raum (DE-588)4184206-6 gnd |
| subject_GND | (DE-588)4168100-9 (DE-588)4164859-6 (DE-588)4184206-6 |
| title | Compactifications of symmetric and locally symmetric spaces |
| title_auth | Compactifications of symmetric and locally symmetric spaces |
| title_exact_search | Compactifications of symmetric and locally symmetric spaces |
| title_full | Compactifications of symmetric and locally symmetric spaces Armand Borel ; Lizhen Ji |
| title_fullStr | Compactifications of symmetric and locally symmetric spaces Armand Borel ; Lizhen Ji |
| title_full_unstemmed | Compactifications of symmetric and locally symmetric spaces Armand Borel ; Lizhen Ji |
| title_short | Compactifications of symmetric and locally symmetric spaces |
| title_sort | compactifications of symmetric and locally symmetric spaces |
| topic | Kompaktifizierung - Lokal symmetrischer Raum Kompaktifizierung - Symmetrischer Raum Compactifications Symmetric spaces Lokal symmetrischer Raum (DE-588)4168100-9 gnd Kompaktifizierung (DE-588)4164859-6 gnd Symmetrischer Raum (DE-588)4184206-6 gnd |
| topic_facet | Kompaktifizierung - Lokal symmetrischer Raum Kompaktifizierung - Symmetrischer Raum Compactifications Symmetric spaces Lokal symmetrischer Raum Kompaktifizierung Symmetrischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013196407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT borelarmand compactificationsofsymmetricandlocallysymmetricspaces AT jilizhen compactificationsofsymmetricandlocallysymmetricspaces |