Rigidity theorems for actions of product groups and countable Borel equivalence relations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
AMS
2005
|
| Schriftenreihe: | American Mathematical Society
Memoirs of the American Mathematical Society ; 833 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "Volume 177, number 833 (first of 4 numbers)." |
| Beschreibung: | VII, 109 S. |
| ISBN: | 0821837710 |
Internformat
MARC
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| 100 | 1 | |a Hjorth, Greg |d 1963-2011 |e Verfasser |0 (DE-588)1146289332 |4 aut | |
| 245 | 1 | 0 | |a Rigidity theorems for actions of product groups and countable Borel equivalence relations |c Greg Hjorth ; Alexander S. Kechris |
| 264 | 1 | |a Providence, RI |b AMS |c 2005 | |
| 300 | |a VII, 109 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a American Mathematical Society : Memoirs of the American Mathematical Society |v 833 | |
| 500 | |a "Volume 177, number 833 (first of 4 numbers)." | ||
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| 700 | 1 | |a Kechris, Alexander S. |d 1946- |e Verfasser |0 (DE-588)109300025 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804133577742352384 |
|---|---|
| adam_text | Contents
Introduction 1
Historical remarks and overview of the main results.
Chapter 0. Preliminaries 9
0A. Actions 9
OB. Equivalence relations 9
0C. Borel notions 10
0D. Measures 11
0E. Borel actions and measures 11
OF. Amenability 12
Chapter 1. Actions of Free Groups and Treeable Equivalence Relations 15
Chapter 2. A Cocycle Reduction Result 21
The ad hoc notion of near hyperbolic.
The main technical device under the assumption of Uo ergodicity (2.2).
Chapter 3. Some Applications 25
Various applications are presented for the structure of countable Borel equiv¬
alence relations under Borel reducibility.
3A. An elementary proof of existence of incomparables 25
3B. Further elementary proofs of theorems of Adams Kechris 27
3C. Elementary proofs of results of Adams and Thomas 28
3D. Relative ergodicity and rigidity results for product group actions 37
Chapter 4. Factoring Homomorphisms 41
A further technical theorem without the assumption of £b ergodicity (4.2).
A theorem on factoring homomorphisms of equivalence relations.
Chapter 5. Further Applications 45
5A. Rigidity results for reducibility and stable orbit equivalence 45
5B. Products of hyperbolic groups 46
Chapter 6. Product Actions, I 49
Non reducibility of mixing product group actions to products of treeable
equivalence relations.
Chapter 7. Product Actions, II 55
A parallel non reducibility result for product actions of Fi x F^, where Fi
has large approximate ergodic dimension and F2 is non amenable, to smaller
products of treeable equivalence relations.
V
vi CONTENTS
Chapter 8. A Final Application 61
Product actions formed from the shift action of F2 and shift actions
formed from products of F i cataloged by Borel reducibility.
Appendix A. Strong Notions of Ergodicity 63
Al. Homomorphisms and relative ergodicity 63
A2. i?o ergodicity and almost invariant sets 63
A3. Almost invariant vectors 66
A4. Bo ergodicity of the shift action 69
A5. Characterizations of amenable and Kazhdan groups 70
A6. Mixing 71
A7. Non orbit equivalent relations 74
Appendix B. Cocycles and Cocycle invariant Functions 77
Bl. Review 77
B2. a invariant functions 78
B3. Q invariant measures 78
The existence in the measurable context for amenable groups. The non
existence in the Baire measurable context and a negative answer to a
question of Weiss.
B4. Maximum two supported measures 85
Appendix C. Actions on Boundaries 87
Cl. Trees 87
C2. Free groups 89
C3. Free products of finite groups 91
C4. Hyperbolic groups 93
Appendix D. /C structured Equivalence Relations 95
Appendix E. Proof of the General Case of Theorem 4.4 99
El. Amenable classes of structures 99
E2. The factoring lemma 101
Bibliography 107
|
| any_adam_object | 1 |
| author | Hjorth, Greg 1963-2011 Kechris, Alexander S. 1946- |
| author_GND | (DE-588)1146289332 (DE-588)109300025 |
| author_facet | Hjorth, Greg 1963-2011 Kechris, Alexander S. 1946- |
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| author_sort | Hjorth, Greg 1963-2011 |
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| dewey-ones | 510 - Mathematics |
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| id | DE-604.BV020017686 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:10:56Z |
| institution | BVB |
| isbn | 0821837710 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013339129 |
| oclc_num | 254302201 |
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| physical | VII, 109 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | AMS |
| record_format | marc |
| series | American Mathematical Society |
| series2 | American Mathematical Society : Memoirs of the American Mathematical Society |
| spelling | Hjorth, Greg 1963-2011 Verfasser (DE-588)1146289332 aut Rigidity theorems for actions of product groups and countable Borel equivalence relations Greg Hjorth ; Alexander S. Kechris Providence, RI AMS 2005 VII, 109 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society : Memoirs of the American Mathematical Society 833 "Volume 177, number 833 (first of 4 numbers)." Borel-Menge Deskriptive Mengenlehre Ergodentheorie - Äquivalenzrelation - Borel-Raum - Produktfamilie Maßtheorie Maßtheorie (DE-588)4074626-4 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Borel-Menge (DE-588)4146323-7 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s Borel-Menge (DE-588)4146323-7 s Maßtheorie (DE-588)4074626-4 s Ergodentheorie (DE-588)4015246-7 s DE-604 Kechris, Alexander S. 1946- Verfasser (DE-588)109300025 aut American Mathematical Society Memoirs of the American Mathematical Society ; 833 (DE-604)BV008000141 833 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013339129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hjorth, Greg 1963-2011 Kechris, Alexander S. 1946- Rigidity theorems for actions of product groups and countable Borel equivalence relations American Mathematical Society Borel-Menge Deskriptive Mengenlehre Ergodentheorie - Äquivalenzrelation - Borel-Raum - Produktfamilie Maßtheorie Maßtheorie (DE-588)4074626-4 gnd Ergodentheorie (DE-588)4015246-7 gnd Borel-Menge (DE-588)4146323-7 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4015246-7 (DE-588)4146323-7 (DE-588)4074715-3 |
| title | Rigidity theorems for actions of product groups and countable Borel equivalence relations |
| title_auth | Rigidity theorems for actions of product groups and countable Borel equivalence relations |
| title_exact_search | Rigidity theorems for actions of product groups and countable Borel equivalence relations |
| title_full | Rigidity theorems for actions of product groups and countable Borel equivalence relations Greg Hjorth ; Alexander S. Kechris |
| title_fullStr | Rigidity theorems for actions of product groups and countable Borel equivalence relations Greg Hjorth ; Alexander S. Kechris |
| title_full_unstemmed | Rigidity theorems for actions of product groups and countable Borel equivalence relations Greg Hjorth ; Alexander S. Kechris |
| title_short | Rigidity theorems for actions of product groups and countable Borel equivalence relations |
| title_sort | rigidity theorems for actions of product groups and countable borel equivalence relations |
| topic | Borel-Menge Deskriptive Mengenlehre Ergodentheorie - Äquivalenzrelation - Borel-Raum - Produktfamilie Maßtheorie Maßtheorie (DE-588)4074626-4 gnd Ergodentheorie (DE-588)4015246-7 gnd Borel-Menge (DE-588)4146323-7 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Borel-Menge Deskriptive Mengenlehre Ergodentheorie - Äquivalenzrelation - Borel-Raum - Produktfamilie Maßtheorie Ergodentheorie Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013339129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT hjorthgreg rigiditytheoremsforactionsofproductgroupsandcountableborelequivalencerelations AT kechrisalexanders rigiditytheoremsforactionsofproductgroupsandcountableborelequivalencerelations |