Chiral Equivariant Cohomology II

Bong H. Lian Brandeis University Andrew R. Linshaw University of Denver Bailin Song University of California Los Angeles

Differential Geometry mathscidoc:1608.10075

Transactions of the American Mathematical Society, 360, 4739-4776, 2008
This is the second in a series of papers on a new equivariant cohomology that takes values in a vertex algebra. In an earlier paper, the first two authors gave a construction of the cohomology functor on the category of O(sg) algebras. The new cohomology theory can be viewed as a kind of "chiralization'' of the classical equivariant cohomology, the latter being defined on the category of $G^*$ algebras a la H. Cartan. In this paper, we further develop the chiral theory by first extending it to allow a much larger class of algebras which we call sg[t] algebras. In the geometrical setting, our principal example of an O(sg) algebra is the chiral de Rham complex Q(M) of a G manifold M. There is an interesting subalgebra of Q(M) which does not admit a full O(sg) algebra structure but retains the structure of an sg[t] algebra, enough for us to define its chiral equivariant cohomology. The latter then turns out to have many surprising features that allows us to delineate a number of interesting geometric aspects of the G manifold M, sometimes in ways that are quite different from the classical theory.
equivariant cohomology, Chiral Equivariant Cohomology, chiral de Rham complex
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  title={Chiral Equivariant Cohomology II},
  author={Bong H. Lian, Andrew R. Linshaw, and Bailin Song},
  booktitle={Transactions of the American Mathematical Society},
Bong H. Lian, Andrew R. Linshaw, and Bailin Song. Chiral Equivariant Cohomology II. 2008. Vol. 360. In Transactions of the American Mathematical Society. pp.4739-4776.
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