Proper Group Actions and the Baum-Connes Conjecture:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2003
|
| Schriftenreihe: | Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The Baum-Connes Conjecture for a group G predicts that a certain index map of analytical nature sets up a natural isomorphism between the G-equivariant K-homology of the universal space EG for proper G-actions and the K-theory of the reduced C* -algebra of the group G. This conjecture has been verified for many classes of groups and is a major target of current research. Its truth im plies the validity of a surprisingly large number of long-standing conjectures in group theory, functional analysis, geometry, and topology. For example, it an swers affirmatively the Idempotent Conjecture, stating that if G is tors ion free, then the complex group algebra qG] has no idempotent other than O and 1, and the Novikov Conjecture, stating that the higher signatures of closed manifolds are oriented homotopy invariants. The beauty and multidisciplinarity ofthis topic motivated an advanced course at the CRM from September 18 to 22, 2001. The topological and algebraic aspects of the Baum-Connes Conjecture were presented by Mislin, while the analytical aspects were presented by Valette. This book contains a revised vers ion of our lecture notes, with emphasis on equivariant homology theories and the analytical assembly map, respectively. Besides our indebtedness to the Centre de Recerca Matematica, thanks are due to Carles Casacuberta, the course coordinator, for making it possible, and to the CRM Secretaries, Consol Roca and Maria Julia, for their assistance |
| Beschreibung: | 1 Online-Ressource (131p) |
| ISBN: | 9783034880893 9783764304089 |
| DOI: | 10.1007/978-3-0348-8089-3 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8089-3 |
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| spelling | Mislin, Guido Verfasser aut Proper Group Actions and the Baum-Connes Conjecture by Guido Mislin, Alain Valette Basel Birkhäuser Basel 2003 1 Online-Ressource (131p) txt rdacontent c rdamedia cr rdacarrier Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica The Baum-Connes Conjecture for a group G predicts that a certain index map of analytical nature sets up a natural isomorphism between the G-equivariant K-homology of the universal space EG for proper G-actions and the K-theory of the reduced C* -algebra of the group G. This conjecture has been verified for many classes of groups and is a major target of current research. Its truth im plies the validity of a surprisingly large number of long-standing conjectures in group theory, functional analysis, geometry, and topology. For example, it an swers affirmatively the Idempotent Conjecture, stating that if G is tors ion free, then the complex group algebra qG] has no idempotent other than O and 1, and the Novikov Conjecture, stating that the higher signatures of closed manifolds are oriented homotopy invariants. The beauty and multidisciplinarity ofthis topic motivated an advanced course at the CRM from September 18 to 22, 2001. The topological and algebraic aspects of the Baum-Connes Conjecture were presented by Mislin, while the analytical aspects were presented by Valette. This book contains a revised vers ion of our lecture notes, with emphasis on equivariant homology theories and the analytical assembly map, respectively. Besides our indebtedness to the Centre de Recerca Matematica, thanks are due to Carles Casacuberta, the course coordinator, for making it possible, and to the CRM Secretaries, Consol Roca and Maria Julia, for their assistance Mathematics Geometry, algebraic Topological Groups Algebraic topology Algebraic Topology Algebraic Geometry Topological Groups, Lie Groups Mathematik Baum-Connes-Vermutung (DE-588)4688506-7 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Baum-Connes-Vermutung (DE-588)4688506-7 s 2\p DE-604 Valette, Alain Sonstige oth https://doi.org/10.1007/978-3-0348-8089-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mislin, Guido Proper Group Actions and the Baum-Connes Conjecture Mathematics Geometry, algebraic Topological Groups Algebraic topology Algebraic Topology Algebraic Geometry Topological Groups, Lie Groups Mathematik Baum-Connes-Vermutung (DE-588)4688506-7 gnd |
| subject_GND | (DE-588)4688506-7 (DE-588)4143413-4 |
| title | Proper Group Actions and the Baum-Connes Conjecture |
| title_auth | Proper Group Actions and the Baum-Connes Conjecture |
| title_exact_search | Proper Group Actions and the Baum-Connes Conjecture |
| title_full | Proper Group Actions and the Baum-Connes Conjecture by Guido Mislin, Alain Valette |
| title_fullStr | Proper Group Actions and the Baum-Connes Conjecture by Guido Mislin, Alain Valette |
| title_full_unstemmed | Proper Group Actions and the Baum-Connes Conjecture by Guido Mislin, Alain Valette |
| title_short | Proper Group Actions and the Baum-Connes Conjecture |
| title_sort | proper group actions and the baum connes conjecture |
| topic | Mathematics Geometry, algebraic Topological Groups Algebraic topology Algebraic Topology Algebraic Geometry Topological Groups, Lie Groups Mathematik Baum-Connes-Vermutung (DE-588)4688506-7 gnd |
| topic_facet | Mathematics Geometry, algebraic Topological Groups Algebraic topology Algebraic Topology Algebraic Geometry Topological Groups, Lie Groups Mathematik Baum-Connes-Vermutung Aufsatzsammlung |
| url | https://doi.org/10.1007/978-3-0348-8089-3 |
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