Gauge fixing and equivariant cohomology

Supersymmetric Gauge Theories, Vortices and Equivariant Cohomology

We construct actions for (p, 0)-and (p, 1)-supersymmetric, 1 ≤ p ≤ 4, two-dimensional gauge theories coupled to non-linear sigma model matter with a Wess-Zumino term. We derive the scalar potential for a large class of these models. We then show that the Euclidean actions of the (2, 0) and (4, 0)-supersymmetric models without Wess-Zumino terms are bounded by topological charges which involve th...

Equivariant Gauge Fixing of SU ( 2 ) Lattice Gauge Theory

I construct a Lattice Gauge Theory (LGT) with discrete Z2 structure group and an equivariant BRST symmetry that for gauge invariant observables is equivalent to the standard SU(2)-LGT. The measure of this Z2-LGT is invariant under all the discrete symmetries of the lattice. The SU(2) structure group of the original LGT is first reduced to an U(1) structure group by an equivariant BRST construct...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

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...