Type of Document	Dissertation
Author	Spakula, Jan
URN	etd-07102008-220512
Title	K-theory of uniform Roe algebras
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Guoliang Yu Committee Chair Bruce Hughes Committee Member Dietmar Bisch Committee Member Gennadi Kasparov Committee Member Thomas Kephart Committee Member
Keywords	coarse geometry C*-algebras K-theory
Date of Defense	2008-05-14
Availability	unrestricted
Abstract We construct a uniform version of the analytic K-homology theory and prove its basic properties such as a Mayer-Vietoris sequence. We show that uniform K-homology is isomorphic to a direct limit of K-theories of certain C*-algebras. Furthermore, we construct an index map (or uniform assembly map) from uniform K-homology into the K-theory of uniform Roe C*-algebras. In an analogy to the coarse Baum--Connes conjecture, this can be viewed as an attempt to provide an algorithm for computing K-theory of uniform Roe algebras. Furthermore, as an application of uniform K-homology, we prove a criterion for amenability. In contrast, we show that uniform Roe C*-algebras of a large class of expanders are not even K-exact. Consequently, their K-theory is in principle not computable by means of exact sequences.
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