Equivariant Cohomology and Localization Formula in Supergeometry
| dc.creator | Lavaud, Pascal | |
| dc.date | 2004-02-04 | |
| dc.date.accessioned | 2026-07-07T05:05:08Z | |
| dc.date.available | 2026-07-07T05:05:08Z | |
| dc.description | Let G be a compact Lie group. Let M be a smooth G-manifold and V --> M be an oriented G-equivariant vector bundle. One defines the spaces of equivariant forms with generalized coefficients on V and M. An equivariant Thom form $θ$ on V is a compactly supported closed equivariant form such that its integral along the fibres is the constant function 1 on M. Such a Thom form was constructed by Mathai and Quillen. Its restriction to M gives a representative of the equivariant Euler class of V. In the supergeometric situation we give proper definitions of all the objects involved. But, in this case a Thom form doesn't always exist. In this article, when the action of G on V is sufficiently non-trivial, we construct such a Thom form with generalized coefficients. We use it to construct an equivariant Euler form of V and to generalize Berline-Vergne's localization formula to the supergeometric situation. | |
| dc.description | 56 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402068 | |
| dc.identifier | http://arxiv.org/abs/math/0402068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70066 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Representation Theory | |
| dc.subject | 14M30; 17B70; 58A50; 58C50 | |
| dc.title | Equivariant Cohomology and Localization Formula in Supergeometry | |
| dc.type | text |