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.
Reihe
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Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-3170-0 (9780821831700)
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Schweitzer Klassifikation
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.
