The connective K theory of semidihedral groups

Abstract

The real connective K-homology of finite groups ko¤(BG), plays a big role in the Gromov-Lawson-Rosenberg (GLR) conjecture. In order to compute them, we can calculate complex connective K-cohomology, ku¤(BG), first and then follow by computing complex connective K-homology, ku¤(BG), or by real connective K-cohomology,ko¤(BG). After we apply the eta-Bockstein spectral sequence to ku¤(BG) or the Greenlees spectral sequence to ko¤(BG), we shall get ko¤(BG). In this thesis, we compute all of them algebraically and explicitly to reduce the di±culties of geometric construction for GLR, especially for semidehedral group of order 16, SD16 , by using the methods developed by Prof.R.R. Bruner and Prof. J.P.C. Greenlees. We also calculate some relations at the stage of connective K-theory between SD16 and its maximal subgroup, (dihedral groups, quaternion groups and cyclic group of order 8).