Abstract/Details

Noncommutative <i>CW</i>-complexes arising from crystallographic groups and their <i>K</i>-theory


2005 2005

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Abstract (summary)

In this thesis we will construct a new class of examples of the so-called noncommutative CW-complexes (NCCW-complexes). First we show that if G is a finite group acting on a CW-complex X by homeomorphisms that permute the cells of the complex, then the crossed product C( X) [special characters omitted] G is an NCCW-complex. This construction applies to the reduced C*-algebra of a group G = [special characters omitted], where H is a finite group and the induced action of H on [special characters omitted] makes [special characters omitted] into an H-CW-complex.

The second thing we give is a technique to systematically compute the K-theory of an n-dimensional NCCW-complex when n equals one or two. This is done using the abstract machinery of algebraic topology. In dimension ≥3 a spectral sequence in K-theory is derived, which converges to the K-theory of the NCCW-complex. Finally explicit computations are made with C*-algebras associated to crystallographic groups.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; CW complexes; Crystallographic; K-theory; Noncommutative
Title
Noncommutative <i>CW</i>-complexes arising from crystallographic groups and their <i>K</i>-theory
Author
McAlister, Erich A.
Number of pages
77
Publication year
2005
Degree date
2005
School code
0051
Source
DAI-B 66/03, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
054204255X, 9780542042553
Advisor
Farsi, Carla
University/institution
University of Colorado at Boulder
University location
United States -- Colorado
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3168286
ProQuest document ID
305010687
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305010687
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