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Index Theory, Eta Forms, and Deligne Cohomology
 
Ulrich Bunke Universität Regensburg, Regensburg, Germany
Index Theory, Eta Forms, and Deligne Cohomology
eBook ISBN:  978-1-4704-0534-2
Product Code:  MEMO/198/928.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
Index Theory, Eta Forms, and Deligne Cohomology
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Index Theory, Eta Forms, and Deligne Cohomology
Ulrich Bunke Universität Regensburg, Regensburg, Germany
eBook ISBN:  978-1-4704-0534-2
Product Code:  MEMO/198/928.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1982009; 120 pp
    MSC: Primary 58; 55

    This paper sets up a language to deal with Dirac operators on manifolds with corners of arbitrary codimension. In particular the author develops a precise theory of boundary reductions.

    The author introduces the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator. Given a Dirac operator on a manifold with boundary faces the author uses the tamings of its boundary reductions in order to turn the operator into a Fredholm operator. Its index is an obstruction against extending the taming from the boundary to the interior. In this way he develops an inductive procedure to associate Fredholm operators to Dirac operators on manifolds with corners and develops the associated obstruction theory.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1
    • Chapter 2. Index theory for families with corners
    • Chapter 3. Analytic obstruction theory
    • Chapter 4. Deligne cohomology valued index theory
  • 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: 1982009; 120 pp
MSC: Primary 58; 55

This paper sets up a language to deal with Dirac operators on manifolds with corners of arbitrary codimension. In particular the author develops a precise theory of boundary reductions.

The author introduces the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator. Given a Dirac operator on a manifold with boundary faces the author uses the tamings of its boundary reductions in order to turn the operator into a Fredholm operator. Its index is an obstruction against extending the taming from the boundary to the interior. In this way he develops an inductive procedure to associate Fredholm operators to Dirac operators on manifolds with corners and develops the associated obstruction theory.

  • Chapters
  • Chapter 1
  • Chapter 2. Index theory for families with corners
  • Chapter 3. Analytic obstruction theory
  • Chapter 4. Deligne cohomology valued index theory
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
Please select which format for which you are requesting permissions.