Introduction to the Baum-Connes Conjecture:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
2002
|
| Series: | Lectures in Mathematics ETH Zürich
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | A quick description of the conjecture The Baum-Connes conjecture is part of Alain Connes' tantalizing "noncommutative geometry" programme [18]. It is in some sense the most "commutative" part of this programme, since it bridges with classical geometry and topology. Let r be a countable group. The Baum-Connes conjecture identifies two objects associated with r, one analytical and one geometrical/topological. The right-hand side of the conjecture, or analytical side, involves the Ktheory of the reduced C*-algebra c;r, which is the C*-algebra generated by r in 2 its left regular representation on the Hilbert space C(r). The K-theory used here, Ki(C;r) for i = 0, 1, is the usual topological K-theory for Banach algebras, as described e.g. in [85]. The left-hand side of the conjecture, or geometrical/topological side RKf(Er) (i=O,I), is the r-equivariant K-homology with r-compact supports of the classifying space Er for proper actions of r. If r is torsion-free, this is the same as the K-homology (with compact supports) of the classifying space Br (or K(r,l) Eilenberg-Mac Lane space). This can be defined purely homotopically |
| Physical Description: | 1 Online-Ressource (X, 104p) |
| ISBN: | 9783034881876 9783764367060 |
| DOI: | 10.1007/978-3-0348-8187-6 |
Staff View
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| isbn | 9783034881876 9783764367060 |
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| spelling | Valette, Alain Verfasser aut Introduction to the Baum-Connes Conjecture by Alain Valette Basel Birkhäuser Basel 2002 1 Online-Ressource (X, 104p) txt rdacontent c rdamedia cr rdacarrier Lectures in Mathematics ETH Zürich A quick description of the conjecture The Baum-Connes conjecture is part of Alain Connes' tantalizing "noncommutative geometry" programme [18]. It is in some sense the most "commutative" part of this programme, since it bridges with classical geometry and topology. Let r be a countable group. The Baum-Connes conjecture identifies two objects associated with r, one analytical and one geometrical/topological. The right-hand side of the conjecture, or analytical side, involves the Ktheory of the reduced C*-algebra c;r, which is the C*-algebra generated by r in 2 its left regular representation on the Hilbert space C(r). The K-theory used here, Ki(C;r) for i = 0, 1, is the usual topological K-theory for Banach algebras, as described e.g. in [85]. The left-hand side of the conjecture, or geometrical/topological side RKf(Er) (i=O,I), is the r-equivariant K-homology with r-compact supports of the classifying space Er for proper actions of r. If r is torsion-free, this is the same as the K-homology (with compact supports) of the classifying space Br (or K(r,l) Eilenberg-Mac Lane space). This can be defined purely homotopically Mathematics Group theory K-theory Topological Groups K-Theory Topological Groups, Lie Groups Group Theory and Generalizations Mathematik KK-Theorie (DE-588)4273845-3 gnd rswk-swf Baum-Connes-Vermutung (DE-588)4688506-7 gnd rswk-swf Baum-Connes-Vermutung (DE-588)4688506-7 s KK-Theorie (DE-588)4273845-3 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-8187-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Valette, Alain Introduction to the Baum-Connes Conjecture Mathematics Group theory K-theory Topological Groups K-Theory Topological Groups, Lie Groups Group Theory and Generalizations Mathematik KK-Theorie (DE-588)4273845-3 gnd Baum-Connes-Vermutung (DE-588)4688506-7 gnd |
| subject_GND | (DE-588)4273845-3 (DE-588)4688506-7 |
| title | Introduction to the Baum-Connes Conjecture |
| title_auth | Introduction to the Baum-Connes Conjecture |
| title_exact_search | Introduction to the Baum-Connes Conjecture |
| title_full | Introduction to the Baum-Connes Conjecture by Alain Valette |
| title_fullStr | Introduction to the Baum-Connes Conjecture by Alain Valette |
| title_full_unstemmed | Introduction to the Baum-Connes Conjecture by Alain Valette |
| title_short | Introduction to the Baum-Connes Conjecture |
| title_sort | introduction to the baum connes conjecture |
| topic | Mathematics Group theory K-theory Topological Groups K-Theory Topological Groups, Lie Groups Group Theory and Generalizations Mathematik KK-Theorie (DE-588)4273845-3 gnd Baum-Connes-Vermutung (DE-588)4688506-7 gnd |
| topic_facet | Mathematics Group theory K-theory Topological Groups K-Theory Topological Groups, Lie Groups Group Theory and Generalizations Mathematik KK-Theorie Baum-Connes-Vermutung |
| url | https://doi.org/10.1007/978-3-0348-8187-6 |
| work_keys_str_mv | AT valettealain introductiontothebaumconnesconjecture |