Abstract

This is the third of a series of papers on a new equivariant cohomology that takes values in a vertex algebra, and contains and generalizes the classical equivariant cohomology of a manifold with a Lie group action à la H. Cartan. In this paper, we compute this cohomology for spheres and show that for any simple connected group $G$, there is a sphere with infinitely many actions of $G$ which have distinct chiral equivariant cohomology, but identical classical equivariant cohomology. Unlike the classical case, the description of the chiral equivariant cohomology of spheres requires a substantial amount of new structural theory, which we fully develop in this paper. This includes a quasi-conformal structure, equivariant homotopy invariance, and the values of this cohomology on homogeneous spaces. These results rely on crucial features of the underlying vertex algebra valued complex that have no classical analogues.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1549-1590
Launched on MUSE
2010-12-02
Open Access
No
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