Higher Franz-Reidemeister Torsion

Download or read book Higher Franz-Reidemeister Torsion written by Kiyoshi Igusa and published by American Mathematical Soc.. This book was released on 2002 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work 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 should provide a useful research and reference tool for specialists working in algebraic topology and $K$-theory.