Noncommutative simplicial complexes and the Baum—Connes conjecture |
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Authors: | J. Cuntz |
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Affiliation: | Mathematisches Institut, Universit?t Münster, Einsteinstr. 62, 48149 Münster, Germany, e-mail: cuntz@math.uni-muenster.de, DE
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Abstract: | We associate a noncommutative C *-algebra with every locally finite simplicial complex.We determine the K-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum—Connes conjecture. Our main technical result determines the algebra generated by the coefficients of a universal projection in an algebraic crossed product by a discrete group , in terms of such a noncommutative algebra associated with a simplicial complex defined by . Submitted: May 2001, Revised: October 2001, Revised: April 2002. |
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