The Novikov Conjecture

Geometry and Algebra

Matthias Kreck, Wolfgang Lück - Collection Oberwolfach Seminars

266 pages, parution le 03/12/2004

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Résumé

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.

L'auteur - Wolfgang Lück

University of Münster, Germany

Sommaire

Introduction
A Motivating Problem
Introduction to the Nopvikov and Borel Conjecture
Normal Bordism Groups
The Signature
The Signature Theorem and the Novikov Conjecture
The Projective Class Group and the Whitehead Group
Whitehead Torsion
The Statement and Consequences of the s-Cobordism Theorem
Sketch of the Proof of the s-Cobordism Theorem
From the Novikov Conjecture to Surgery
Surgery Below the Middle Dimension I: An Example
Surgery Below the Middle Dimension II: Systematically
Surgery in the Middle Dimension I
Surgery in the Middle Dimension II
Surgery in the Middle Dimension III
An Assembly Map
The Novikov Conjecture for Zⁿ
Poincaré Duality and Algebraic L-Groups
Spectra
Classifying Spaces of Families
Equivariant Homology Theories and the Meta-Conjecture
The Farrell-Jones Conjecture
The Baum-Connes Conjecture
Relating the Novikov, the Farrell-Jones and the Baum-Connes Conjectures
Miscellaneous
Exercises
Hints to the Solutions of the Exercises
References
Index
Notation

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Matthias Kreck, Wolfgang Lück
Collection	Oberwolfach Seminars
Parution	03/12/2004
Nb. de pages	266
Format	17 x 24
Couverture	Broché
Poids	545g
Intérieur	Noir et Blanc
EAN13	9783764371418