The Novikov Conjecture : Geometry and Algebra

Matthias Kreck

ISBN 10: 3764371412 / ISBN 13: 9783764371418

Published by Birkhäuser, Birkhäuser, 2004

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783764371418

Bibliographic Details

• Title: The Novikov Conjecture : Geometry and Algebra
• Publisher: Birkhäuser, Birkhäuser
• Publication Date: 2004
• Language: English
• ISBN 10: 3764371412
• ISBN 13: 9783764371418
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 16D millimeters 254 millimeters width by 178 millimeters height by 16 millimeters depth
• Weight: 547 grams

About this title

Synopsis

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.

Review

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)