ENGLISH

Index theory, eta forms, and Deligne cohomology

By Ulrich Bunke

Book information

Publisher
Amer Mathematical Society
Year
2009
ISBN
0821842846, 978-0-8218-4284-3
Language
english
Format
PDF
Filesize
828 kB (848206 bytes)
Series
Memoirs of the American Mathematical Society 0928
Pages
134\134
Library
kolxoz
Time added
2015-12-12 14:00:00

Description

This paper sets up a language to deal with Dirac operators on manifolds with corners of arbitrary co-dimension. 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

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