9783764367060 - Introduction To The Baum-Connes Conjecture (Lectures in Mathematics. ETH Zürich) von Valette, Alain (6 Ergebnisse)

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Zustand: New. The Baum-Connes conjecture is part of A Connes' non-commutative geometry programme. This book presents an introduction to the Baum-Connes conjecture. It starts by defining the objects in both sides of the conjecture, then the assembly map which connects them. It illustrates the main tool to attack the conjecture (Kasparov's theory). Series: Lectures in Mathematics. ETH Zurich. Num Pages: 114 pages, biography. BIC Classification: PBF; PBM. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 173 x 244 x 11. Weight in Grams: 222. . 2002. 2002nd Edition. paperback. . . . . Books ship from the US and Ireland.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.