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