Title:	Morava K-theory of classifying spaces 
Author: Björn Schuster
Date:   13 December 2006
Status: Habilitationsschrift, 124+vi pp.

Abstract:
The theme of this book is calculating Morava K-theory of classifying spaces, 
in particular of finite groups. This topic has roots both in homotopy theory 
and in group cohomology; in fact, given the lack of a proper geometric model 
for Morava K-theory, many calculations have the flavour of group cohomology 
with complicated coefficients. 

There are many such computations in the literature, and apart from offering 
some new ones, we also give a survey of the known results.

The first part of the book contains the background for the calculations 
carried out in the later chapters. For most of the theory presented here 
we do not claim originality. A new feature though is an adaptation of the 
Rothenberg-Steenrod spectral sequence to central products of groups; this 
leads to various simplifications of existing work.

In Part 2 the techniques of Part 1 are applied to concrete calculations. 
The first of its chapters is intended as a survey of results scattered over 
the literature. Some new proofs are given, but mostly the results are just 
stated. Examples of groups whose Morava K-theory is completely determined 
by the representation ring of the group are given next. The following chapter 
concentrates on the prime 2 and contains new calculations. In particular, we 
determine the Morava K-theory of the groups of order 32, although in some
cases we rely on machine computations, which restricts the results to K(2).

Since it seemed to fit with the rest of the material, an earlier paper on 
the structure of the Morava K-theory of an elementary abelian group as a 
module for its automorphism group was also reproduced. The book ends with a 
few preliminary observations on discrete groups.