The Novikov Conjecture: Geometry And Algebra

These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given. Finally, the most recent developments concerning these conjectures are surveyed, including a detailed status report.
The prerequisites consist of a solid knowledge of the basics about manifolds, vector bundles, (co-) homology and characteristic classes.

From the reviews:

This very readable book provides an excellent introduction to the circle of ideas related to the Novikov conjecture.

Monatshefte für Mathematik

“Overall, the book is very suitable both as an introduction and as a reference, and finds exactly the right balance between detail, comprehensiveness and length of the presentation. It is recommended to everyone with a background in algebraic topology who wants to learn about one or some of the aspects covered.”(MATHEMATICAL REVIEWS)