Generalized Equivariant Cohomology and Stratifications

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Affine Stratifications and equivariant vector bundles on

of the Dissertation Affine Stratifications and equivariant vector bundles on the moduli of principally polarized abelian varieties by Anant Atyam Doctor of Philosophy in Mathematics Stony Brook University 2014 We explicitly construct a locally closed affine stratification of the coarse moduli space of principally polarized complex abelian four folds A4 and using [32], produce an upper bound for...

Equivariant cohomology and equivariant intersection theory

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain explicit descriptions of cohomology or Chow rings of certain manifolds with group actions which ar...

Equivariant Cohomology and Resolution

The ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution tower’ which projects to a resolution, with iterated boundary fibration, of the quotient. Equivaria...

The Equivariant Cohomology Theory of Twisted Generalized Complex Manifolds

It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If th...