dc.creator | Spakula, Jan | |
dc.date.accessioned | 2020-08-22T17:20:27Z | |
dc.date.available | 2010-07-17 | |
dc.date.issued | 2008-07-17 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-07102008-220512 | |
dc.identifier.uri | http://hdl.handle.net/1803/12888 | |
dc.description.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. | |
dc.format.mimetype | application/pdf | |
dc.subject | coarse geometry | |
dc.subject | C*-algebras | |
dc.subject | K-theory | |
dc.title | K-theory of uniform Roe algebras | |
dc.type | dissertation | |
dc.contributor.committeeMember | Dietmar Bisch | |
dc.contributor.committeeMember | Bruce Hughes | |
dc.contributor.committeeMember | Gennadi Kasparov | |
dc.contributor.committeeMember | Thomas Kephart | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2010-07-17 | |
local.embargo.lift | 2010-07-17 | |
dc.contributor.committeeChair | Guoliang Yu | |