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Diffeomorphisms and Noncommutative Analytic Torsion
 
John Lott University of Michigan, Ann Arbor, Ann Arbor, MI
Diffeomorphisms and Noncommutative Analytic Torsion
eBook ISBN:  978-1-4704-0264-8
Product Code:  MEMO/141/673.E
List Price: $46.00
MAA Member Price: $41.40
AMS Member Price: $27.60
Diffeomorphisms and Noncommutative Analytic Torsion
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Diffeomorphisms and Noncommutative Analytic Torsion
John Lott University of Michigan, Ann Arbor, Ann Arbor, MI
eBook ISBN:  978-1-4704-0264-8
Product Code:  MEMO/141/673.E
List Price: $46.00
MAA Member Price: $41.40
AMS Member Price: $27.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1411999; 56 pp
    MSC: Primary 58;

    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
     
     
    • Chapters
    • 1. Introduction
    • 2. Noncommutative bundle theory
    • 3. Groups and covering spaces
    • 4. $\mathfrak {B}$-Hermitian metrics and characteristic classes
    • 5. Noncommutative superconnections
    • 6. Fiber bundles
    • 7. Diffeomorphism groups
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1411999; 56 pp
MSC: Primary 58;

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.

  • Chapters
  • 1. Introduction
  • 2. Noncommutative bundle theory
  • 3. Groups and covering spaces
  • 4. $\mathfrak {B}$-Hermitian metrics and characteristic classes
  • 5. Noncommutative superconnections
  • 6. Fiber bundles
  • 7. Diffeomorphism groups
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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