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Diffeomorphisms and Noncommutative Analytic Torsion
John Lott, University of Michigan, Ann Arbor, MI
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Memoirs of the American Mathematical Society
1999; 56 pp; softcover
Volume: 141
ISBN-10: 0-8218-1189-4
ISBN-13: 978-0-8218-1189-4
List Price: US$43
Individual Members: US$25.80
Institutional Members: US$34.40
Order Code: MEMO/141/673
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Abstract. We prove an index theorem concerning the pushforward of flat \({\mathfrak B}\)-vector bundles, where \({\mathfrak B}\) is an appropriate algebra. We construct an associated analytic torsion form \({\mathcal T}\). If \(Z\) is a smooth closed aspherical manifold, we show that \({\mathcal T}\) gives invariants of \(\pi_*(\mathrm{Diff}(Z))\).

Readership

Graduate students and research mathematicians working in global analysis and analysis on manifolds.

Table of Contents

  • Introduction
  • Noncommutative bundle theory
  • Groups and covering spaces
  • \(\mathfrak B\)-Hermitian metrics and characteristic classes
  • Noncommutative superconnections
  • Fiber bundles
  • Diffeomorphism groups
  • References
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