T-equivariant cohomology of cell complexes and the case of infinite
Grassmannians
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abstract

In 1998, Goresky, Kottwitz, and MacPherson showed that for certain spaces X
equipped with a torus action, the T-equivariant cohomology ring of X can be
described by combinatorial data obtained from its orbit decomposition. Thus,
their theory transforms calculations of the equivariant topology of X to those
of the combinatorics of the orbit decomposition. Since then, many authors have
studied this interplay between topology and combinatorics. In this paper, we
generalize the theorem of Goresky, Kottwitz, and MacPherson to the (possibly
infinite-dimensional) setting where X is any equivariant cell complex with only
even-dimensional cells and isolated T-fixed points, along with some additional
technical hypotheses on the gluing maps. This generalization includes many new
examples which have not yet been studied by GKM theory, including homogeneous
spaces of a loop group LG.