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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Introduction to the Baum-Connes Conjecture

Introduction to the Baum-Connes Conjecture

Valette, Alain

Paperback

Series: Lectures in Mathematics. Eth Zürich

AlgebraGeometry

ISBN10: 3764367067
ISBN13: 9783764367060
Publisher: Birkhauser
Published: Apr 1 2002
Pages: 104
Weight: 0.52
Height: 0.33 Width: 6.72 Depth: 9.41
Language: English
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.

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