Index theory, eta forms, and Deligne cohomology
| dc.creator | Bunke, U. | |
| dc.date | 2002-01-14 | |
| dc.date | 2006-09-21 | |
| dc.date.accessioned | 2026-07-07T06:35:28Z | |
| dc.date.available | 2026-07-07T06:35:28Z | |
| dc.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. | |
| dc.description | Revised version (some arguments expanded and examples added) 147 pages | |
| dc.identifier | https://arxiv.org/abs/math/0201112 | |
| dc.identifier | http://arxiv.org/abs/math/0201112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99800 | |
| dc.subject | Differential Geometry | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 58J28 | |
| dc.title | Index theory, eta forms, and Deligne cohomology | |
| dc.type | text |