Index theory, eta forms, and Deligne cohomology

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

The Chern classes of a K-theory class which is represented by a vector bundle with connection admit refinements to Cheeger-Simons classes in Deligne cohomology. In the present paper we consider similar refinements in the case where the classes in K-theory are represented by geometric families of Dirac operators. In low dimensions these refinements correspond to the exponentiated eta-invariant, the determinant line bundle with Quillen metric and Bismut-Freed connection, and Lott's index gerbe with connection and curving. We give a unified treatement of these cases as well as their higher generalizations. Our main technical tool is a variant of local index theory for Dirac operators of families of manifolds with corners.
Revised version (some arguments expanded and examples added) 147 pages

Keywords

Differential Geometry, K-Theory and Homology, 58J28

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/99800

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0201112
 http://arxiv.org/abs/math/0201112

Collections

arXiv