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