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Connes-Chern Character for Manifolds with Boundary and Eta Cochains
 
Matthias Lesch Universität Bonn, Bonn, Germany
Henri Moscovici Ohio State University, Columbus, OH
Markus J. Pflaum University of Colorado, Boulder, Boulder, CO
Connes-Chern Character for Manifolds with Boundary and Eta Cochains
eBook ISBN:  978-0-8218-9209-1
Product Code:  MEMO/220/1036.E
List Price: $67.00
MAA Member Price: $60.30
AMS Member Price: $40.20
Connes-Chern Character for Manifolds with Boundary and Eta Cochains
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Connes-Chern Character for Manifolds with Boundary and Eta Cochains
Matthias Lesch Universität Bonn, Bonn, Germany
Henri Moscovici Ohio State University, Columbus, OH
Markus J. Pflaum University of Colorado, Boulder, Boulder, CO
eBook ISBN:  978-0-8218-9209-1
Product Code:  MEMO/220/1036.E
List Price: $67.00
MAA Member Price: $60.30
AMS Member Price: $40.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2202012; 92 pp
    MSC: Primary 58; 46;

    The authors express the Connes-Chern of the Dirac operator associated to a b-metric on a manifold with boundary in terms of a retracted cocycle in relative cyclic cohomology, whose expression depends on a scaling/cut-off parameter. Blowing-up the metric one recovers the pair of characteristic currents that represent the corresponding de Rham relative homology class, while the blow-down yields a relative cocycle whose expression involves higher eta cochains and their b-analogues. The corresponding pairing formulæ, with relative K-theory classes, capture information about the boundary and allow to derive geometric consequences. As a by-product, the authors show that the generalized Atiyah-Patodi-Singer pairing introduced by Getzler and Wu is necessarily restricted to almost flat bundles.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Preliminaries
    • 2. The b-Analogue of the Entire Chern Character
    • 3. Heat Kernel and Resolvent Estimates
    • 4. The Main Results
  • 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: 2202012; 92 pp
MSC: Primary 58; 46;

The authors express the Connes-Chern of the Dirac operator associated to a b-metric on a manifold with boundary in terms of a retracted cocycle in relative cyclic cohomology, whose expression depends on a scaling/cut-off parameter. Blowing-up the metric one recovers the pair of characteristic currents that represent the corresponding de Rham relative homology class, while the blow-down yields a relative cocycle whose expression involves higher eta cochains and their b-analogues. The corresponding pairing formulæ, with relative K-theory classes, capture information about the boundary and allow to derive geometric consequences. As a by-product, the authors show that the generalized Atiyah-Patodi-Singer pairing introduced by Getzler and Wu is necessarily restricted to almost flat bundles.

  • Chapters
  • Introduction
  • 1. Preliminaries
  • 2. The b-Analogue of the Entire Chern Character
  • 3. Heat Kernel and Resolvent Estimates
  • 4. The Main Results
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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