On the relationship of gerbes to the odd families index theorem
| dc.creator | Carey, Alan L. | |
| dc.creator | Wang, Bai-Ling | |
| dc.date | 2004-07-14 | |
| dc.date | 2006-02-20 | |
| dc.date.accessioned | 2026-07-07T06:38:40Z | |
| dc.date.available | 2026-07-07T06:38:40Z | |
| dc.description | The goal of this paper is to apply the universal gerbe of \cite{CMi1} and \cite{CMi2} to give an alternative, simple and more unified view of the relationship between index theory and gerbes. We discuss determinant bundle gerbes \cite{CMMi1} and the index gerbe of \cite{L} for the case of families of Dirac operators on odd dimensional closed manifolds. The method also works for a family of Dirac operators on odd dimensional manifolds with boundary, for a pair of Melrose-Piazza's $Cl(1)$-spectral sections for a family of Dirac operators on even dimensional closed manifolds with vanishing index in $K$-theory and, in a simple case, for manifolds with corners. The common feature of these bundle gerbes is that there exists a canonical bundle gerbe connection whose curving is given by the degree 2 part of the even eta-form (up to a locally defined exact form) arising from the local family index theorem. | |
| dc.description | 26 pages, no figures; to appear in Journ. of Geom. and Phys | |
| dc.identifier | https://arxiv.org/abs/math/0407243 | |
| dc.identifier | http://arxiv.org/abs/math/0407243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100816 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 57J52,55R65,19K56,58J28 | |
| dc.title | On the relationship of gerbes to the odd families index theorem | |
| dc.type | text |