Memoirs of the American Mathematical Society 2009; 120 pp; softcover Volume: 198 ISBN10: 0821842846 ISBN13: 9780821842843 List Price: US$67 Individual Members: US$40.20 Institutional Members: US$53.60 Order Code: MEMO/198/928
 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  Introduction
 Index theory for families with corners
 Analytic obstruction theory
 Deligne cohomology valued index theory
 Bibliography
 Index
