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• W2160649120 abstract "Let T be a compact torus and X a nice compact T-space (say a manifold or variety). We introduce a functor assigning to X a GKM-sheaf F_X over a GKM-hypergraph G_X. Under the condition that X is equivariantly formal, the ring of global sections of F_X are identified with the equivariant cohomology, H_T^*(X; C). We show that GKM-sheaves provide a general framework able to incorporate numerous constructions in the GKM-theory literature. In the second half of the paper we apply these ideas to study the equivariant topology of the representation variety R_K := Hom(pi_1(S), K) under conjugation by K, where S is a nonorientable surface and K is a compact connected Lie group. We prove that R_{SU(3)} is equivariantly formal for all S and compute its equivariant cohomology. . We also produce conjectural betti number formulas for some other Lie groups." @default.
• W2160649120 created "2016-06-24" @default.
• W2160649120 creator A5052511191 @default.
• W2160649120 date "2010-08-09" @default.
• W2160649120 modified "2023-09-27" @default.
• W2160649120 title "GKM sheaves and nonorientable surface group representations" @default.
• W2160649120 cites W1495410784 @default.
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