{"product_id":"introduction-to-the-baum-connes-conjecture-von-alain-valette","title":"Introduction to the Baum-Connes Conjecture","description":"\u003cp\u003eA 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783764367060\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783764367060","offer_id":49593045614917,"sku":"9783764367060","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/0e6c510e-615e-48d5-b776-97332637225a.jpg?v=1772086446","url":"https:\/\/shop.autorenwelt.de\/products\/introduction-to-the-baum-connes-conjecture-von-alain-valette","provider":"Autorenwelt Shop","version":"1.0","type":"link"}