Equivariant cohomology theories

Exercises in Equivariant Cohomology and Topological Theories

Before going into the subject of this talk, I would like to describe some concrete exercises done by Claude and I which represent a very small portion of the numerous discussions we had, mostly by exchange of letters. We happened to be both guests of the CERN theory division during the academic year 19721973. The perturbative renormalization of gauge theories was still a hot subject, and, where...

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 Formal Group Laws and Complex Oriented Cohomology Theories

The article gives an introduction to equivariant formal group laws, and explains its relevance to complex oriented cohomol-ogy theories in general and to complex cobordism in particular.

Equivariant de Rham cohomology and gauged field theories

5 Mapping supermanifolds and the functor of points formalism 31 5.1 Internal hom objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.2 The functor of points formalism . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.3 The supermanifold of endomorphisms of R0|1 . . . . . . . . . . . . . . . . . . 36 5.4 Vector bundles on supermanifolds . . . . . . . . . . . . . . . ....

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology