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Title page for ETD etd-07102008-220512


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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