Computation of generalized equivariant cohomologies of Kac-Moody flag varieties

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dc.creatorHarada, Megumi
dc.creatorHenriques, Andre
dc.creatorHolm, Tara S.
dc.date2004-09-17
dc.date.accessioned2026-07-07T05:12:15Z
dc.date.available2026-07-07T05:12:15Z
dc.descriptionIn 1998, Goresky, Kottwitz, and MacPherson showed that for certain projective varieties X equipped with an algebraic action of a complex torus T, the equivariant cohomology ring H_T(X) can be described by combinatorial data obtained from its orbit decomposition. In this paper, we generalize their theorem in three different ways. First, our group G need not be a torus. Second, our space X is an equivariant stratified space, along with some additional hypotheses on the attaching maps. Third, and most important, we allow for generalized equivariant cohomology theories E_G^* instead of H_T^*. For these spaces, we give a combinatorial description of E_G(X) as a subring of \prod E_G(F_i), where the F_i are certain invariant subspaces of X. Our main examples are the flag varieties G/P of Kac-Moody groups G, with the action of the torus of G. In this context, the F_i are the T-fixed points and E_G^* is a T-equivariant complex oriented cohomology theory, such as H_T^*, K_T^* or MU_T^*. We detail several explicit examples.
dc.description19 pages, 6 figures, this is a new and completely modified version of DG/0402079
dc.identifierhttps://arxiv.org/abs/math/0409305
dc.identifierhttp://arxiv.org/abs/math/0409305
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72512
dc.subjectAlgebraic Topology
dc.subjectK-Theory and Homology
dc.subject55N91; 22E65; 53D20
dc.titleComputation of generalized equivariant cohomologies of Kac-Moody flag varieties
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