Overview

The book is devoted to the theory of topological higher Franz-Reidemeister torsion in $K$-theory. The author defines the higher Franz-Reidemeister torsion based on Volodin's $K$-theory and Borel's regulator map. He describes its properties and generalizations and studies the relation between the higher Franz-Reidemeister torsion and other torsions used in $K$-theory: Whitehead torsion and Ray-Singer torsion. He also presents methods of computing higher Franz-Reidemeister torsion, illustrates them with numerous examples, and describes various applications of higher Franz-Reidemeister torsion, particularly for the study of homology of mapping class groups. Packed with up-to-date information, the book provides a unique research and reference tool for specialists working in algebraic topology and $K$-theory.

Full Product Details

Author:   Kiyoshi Igusa
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 31
Weight:   0.907kg
ISBN:  

9780821831700

ISBN 10:   0821831704
Pages:   392
Publication Date:   30 December 2002
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
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Table of Contents

Cocycles in Volodin $K$-theory Spaces of matrices and higher Franz-Reidemeister torsion A model for the Whitehead spaces Morse theory and filtered chain complexes Homotopy type of the Whitehead space The framing principle and Bokstedt's theorem Proof of complexified Bokstedt theorem Framed graphs Bibliography Index.

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