This volume stems from an Oberwolfach seminar that was held in January 2004. It will attract attention from both beginners and specialists. Postgraduate students will find here a very clearly described motivation for the Novikov conjecture and they will be pleased by the fact that many notions, many of which they may not be familiar with, are described in the subsequent chapters with quite a few details. There are chapters treating the signature and the signature theorem, cobordism theory, the Whitehead group and the Whitehead torsion, several chapters concerning the surgery, a chapter on spectra and a chapter on classifying spaces of families. The book includes a proof of the Novikov conjecture for finitely generated free abelian groups.

It is very useful that all this material is concentrated in one volume but what I mostly appreciate is that the reader always knows why he or she is studying this or that theory and where these theories have their applications. There is no doubt that it is very stimulating. For better understanding, the book concludes with a whole chapter of exercises and one more chapter containing hints to these exercises. The book has an index as well as an index of notations and a long list of references consisting of 258 items. On the other hand, a specialist in topology will find here information about the recent developments concerning the Novikov conjecture. A lot of attention is also devoted to other conjectures closely related to the Novikov conjecture, especially to the Farell-Jones and Baum-Connes conjectures.

Reviewer:

jiva