# Matthias Kreck, Wolfgang Luck - The Novikov Conjecture: Geometry and Algebra

Matthias Kreck, Wolfgang Luck - The Novikov Conjecture: Geometry and Algebra

Birkh?user Basel | 2005 | ISBN: 3764371412 | Pages: 266 | File type: PDF | 1 mb

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.

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