Index theory, eta forms, and Deligne cohomology
About this Title
Publication: Memoirs of the American Mathematical Society
Publication Year 2009: Volume 198, Number 928
ISBNs: 978-0-8218-4284-3 (print); 978-1-4704-0534-2 (online)
MathSciNet review: 2191484
MSC (2000): Primary 58J22; Secondary 53C08, 55S35, 58J28
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
- Chapter 1
- Chapter 2. Index theory for families with corners
- Chapter 3. Analytic obstruction theory
- Chapter 4. Deligne cohomology valued index theory