Index Theory, Eta Forms, and Deligne Cohomology

Download or read book Index Theory, Eta Forms, and Deligne Cohomology written by Ulrich Bunke and published by American Mathematical Soc.. This book was released on 2009-03-06 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.