Oberwolfach Seminars: Geometry and Algebra

Kreck, Matthias; Lück, Wolfgang

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.

Details

Published by: Birkhäuser

Publication Date: 2004-11-22

Format: Paperback

ISBN-13: 9783764371418

DOI: 10.1007/b137100

Dimensions: 254cm x178cm

Pages: 266