Extended manifolds and extended equivariant cohomology

Details Extended manifolds and extended equivariant cohomology Extended manifolds and extended equivariant cohomology

2006-08-13

arxiv.org/abs/math/0608319v3

Mathematics

Differential Geometry

Revised version. Definition 5.1.1 and examples 5.6.2 and 7.2.7 corrected. 36 pages

Scientific paper

We define the category of manifolds with extended tangent bundles, we study their symmetries and we consider the analogue of equivariant cohomology for actions of Lie groups in this category. We show that when the action preserves the splitting of the extended tangent bundle, our definition of extended equivariant cohomology agrees with the twisted equivariant de Rham model of Cartan, and for this case we show that there is localization at the fixed point set, \`a la Atiyah-Bott.

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