Torus actions and their applications in topology and combinatorics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2002]
|
| Schriftenreihe: | University lecture series
Volume 24 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 144 Seiten Diagramme |
| ISBN: | 0821831860 9780821831861 |
Internformat
MARC
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| 245 | 1 | 0 | |a Torus actions and their applications in topology and combinatorics |c Victor M. Buchstaber ; Taras E. Panov |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2002] | |
| 264 | 4 | |c © 2002 | |
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Datensatz im Suchindex
| _version_ | 1804129250680242176 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter 1. Polytopes 7
1.1. Definitions and main constructions 7
1.2. Face vectors and Dehn Sommerville equations 11
1.3. Theg theorem 15
1.4. Upper Bound and Lower Bound theorems 18
1.5. Stanley Reisner face rings of simple polytopes 20
Chapter 2. Topology and combinatorics of simplicial complexes 21
2.1. Abstract simplicial complexes and polyhedrons 21
2.2. Basic PL topology, and operations with simplicial complexes 23
2.3. Simplicial spheres 28
2.4. Triangulated manifolds 29
2.5. Bistellar moves 31
Chapter 3. Commutative and homological algebra of simplicial complexes 35
3.1. Stanley Reisner face rings of simplicial complexes 35
3.2. Cohen Macaulay rings and complexes 38
3.3. Homological algebra background 40
3.4. Homological properties of face rings: Tor algebras and Betti numbers 42
3.5. Gorenstein complexes and Dehn Sommerville equations 46
Chapter 4. Cubical complexes 49
4.1. Definitions and cubical maps 49
4.2. Cubical subdivisions of simple polytopes and simplicial complexes 50
Chapter 5. Tone and quasitoric manifolds 57
5.1. Toric varieties 57
5.2. Quasitoric manifolds 63
5.3. Stably complex structures, and quasitoric representatives in cobordism
classes 69
5.4. Combinatorial formulae for Hirzebruch genera of quasitoric manifolds 74
5.5. Classification problems 82
Chapter 6. Moment angle complexes 85
6.1. Moment angle manifolds Zp denned by simple polytopes 85
6.2. General moment angle complexes Zfc 87
6.3. Cell decompositions of moment angle complexes 89
6.4. Moment angle complexes corresponding to joins, connected sums and
bistellar moves 92
vii
viii CONTENTS
6.5. Borel constructions and Davis Januszkiewicz space 94
6.6. Walk around the construction of Zk ¦ generalizations, analogues and
additional comments 97
Chapter 7. Cohomology of moment angle complexes and combinatorics of
triangulated manifolds 101
7.1. The Eilenberg Moore spectral sequence 101
7.2. Cohomology algebra of ZK 102
7.3. Bigraded Betti numbers of Zk the case of general K 106
7.4. Bigraded Betti numbers of Zk ¦ the case of spherical K 110
7.5. Partial quotients of Zp 113
7.6. Bigraded Poincare duality and Dehn Sommerville equations 117
Chapter 8. Cohomology rings of subspace arrangement complements 125
8.1. General arrangements and their complements 125
8.2. Coordinate subspace arrangements and the cohomology of Zk 127
8.3. Diagonal subspace arrangements and the cohomology of Q,Zk 133
Bibliography 135
Index 141
|
| any_adam_object | 1 |
| author | Buchštaber, Viktor Matveevič 1943- Panov, Taras E. 1975- |
| author_GND | (DE-588)1067767517 (DE-588)173549888 |
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| dewey-full | 514/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.3 |
| dewey-search | 514/.3 |
| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014371334 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:02:09Z |
| institution | BVB |
| isbn | 0821831860 9780821831861 |
| language | English |
| lccn | 2002018243 |
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| physical | viii, 144 Seiten Diagramme |
| publishDate | 2002 |
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| series | University lecture series |
| series2 | University lecture series |
| spelling | Buchštaber, Viktor Matveevič 1943- Verfasser (DE-588)1067767517 aut Torus actions and their applications in topology and combinatorics Victor M. Buchstaber ; Taras E. Panov Providence, Rhode Island American Mathematical Society [2002] © 2002 viii, 144 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 24 Combinatorial analysis Topological spaces Torus (Geometry) Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Torus (DE-588)4185738-0 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Torus (DE-588)4185738-0 s Topologischer Raum (DE-588)4137586-5 s Kombinatorische Analysis (DE-588)4164746-4 s DE-604 Panov, Taras E. 1975- Verfasser (DE-588)173549888 aut Erscheint auch als Online-Ausgabe 978-1-4704-2171-7 University lecture series Volume 24 (DE-604)BV004153846 24 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009844718&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buchštaber, Viktor Matveevič 1943- Panov, Taras E. 1975- Torus actions and their applications in topology and combinatorics University lecture series Combinatorial analysis Topological spaces Torus (Geometry) Topologischer Raum (DE-588)4137586-5 gnd Torus (DE-588)4185738-0 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4137586-5 (DE-588)4185738-0 (DE-588)4164746-4 |
| title | Torus actions and their applications in topology and combinatorics |
| title_auth | Torus actions and their applications in topology and combinatorics |
| title_exact_search | Torus actions and their applications in topology and combinatorics |
| title_full | Torus actions and their applications in topology and combinatorics Victor M. Buchstaber ; Taras E. Panov |
| title_fullStr | Torus actions and their applications in topology and combinatorics Victor M. Buchstaber ; Taras E. Panov |
| title_full_unstemmed | Torus actions and their applications in topology and combinatorics Victor M. Buchstaber ; Taras E. Panov |
| title_short | Torus actions and their applications in topology and combinatorics |
| title_sort | torus actions and their applications in topology and combinatorics |
| topic | Combinatorial analysis Topological spaces Torus (Geometry) Topologischer Raum (DE-588)4137586-5 gnd Torus (DE-588)4185738-0 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Combinatorial analysis Topological spaces Torus (Geometry) Topologischer Raum Torus Kombinatorische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009844718&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
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