Buch, Englisch, 104 Seiten, Paperback, Format (B × H): 170 mm x 244 mm, Gewicht: 222 g
Buch, Englisch, 104 Seiten, Paperback, Format (B × H): 170 mm x 244 mm, Gewicht: 222 g
Reihe: Lectures in Mathematics. ETH Zürich
ISBN: 978-3-7643-6706-0
Verlag: Springer
A quick description of the conjecture The Baum-Connes conjecture is part of Alain Connes'tantalizing "noncommuta tive 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 K theory 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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Mathematik | Informatik Mathematik Geometrie
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Algebra Homologische Algebra
Weitere Infos & Material
1 Idempotents in Group Algebras.- 2 The Baum-Connes Conjecture.- 3K-theory for (Group) C*-algebras.- 4 Classifying Spaces andK-homology.- 5 EquivariantKK-theory.- 6 The Analytical Assembly Map.- 7 Some Examples of the Assembly Map.- 8 Property (RD).- 9 The Dirac-dual Dirac Method.- 10 Lafforgue’sKKBan
Theory.- G. Mislin: On the Classifying Space for Proper Actions.- A.1 The topologist’s model.- A.2 The analyst’s model.- A.4 Spectra.
