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Higher Franz-Reidemeister Torsion
Kiyoshi Igusa, Brandeis University, Waltham, MA
A co-publication of the AMS and International Press.
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AMS/IP Studies in Advanced Mathematics
2002; 370 pp; hardcover
Volume: 31
ISBN-10: 0-8218-3170-4
ISBN-13: 978-0-8218-3170-0
List Price: US$91
Member Price: US$72.80
Order Code: AMSIP/31
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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.

Titles in this series are co-published with International Press, Cambridge, MA.

Readership

Researchers and advanced graduate students in algebraic topology, \(K\)-theory, and their applications.

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 Bökstedt's theorem
  • Proof of complexified Bökstedt theorem
  • Framed graphs
  • Bibliography
  • Index
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