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- W3156991175 abstract "In this paper, we define `simplicial GKM orbifold complexes' and `simplicial GKM graph complexes'. We study some of their topological and combinatorial properties. We discuss some necessary conditions to confirm an invariant $q$-cell structure on a simplicial GKM orbifold complex. We prove Thom isomorphism theorem for orbifold $G$-vector bundles for equivariant cohomology and equivariant K-theory with rational coefficients. We use this to extend the main result of Harada-Henriques-Holm (2005) to the category of $G$-spaces equipped with `singular invariant stratification'. Then we introduce an equivalent definition of weighted Grassmann orbifolds which were introduced by Corti and Reid (2002) and explicitly studied by Abe and Matsumura (2015) to compute their equivariant cohomology with rational coefficients. These orbifolds are a generalization of Grassmann manifolds. We study their different $q$-cell structures and discuss some necessary conditions to determine if they have invariant CW-structures. We employ the techniques from the first part to study some generalized equivariant cohomology theories of weighted Grassmann orbifolds. We introduce `divisive' weighted Grassmann orbifolds and compute their equivariant cohomology, equivariant K-theory and equivariant cobordism ring with integer coefficients. We discuss Schubert calculus for the equivariant cohomology ring and show how to compute the corresponding structure constants with integer coefficients." @default.
- W3156991175 created "2021-04-26" @default.
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- W3156991175 date "2021-04-21" @default.
- W3156991175 modified "2023-09-27" @default.
- W3156991175 title "Integral generalized equivariant cohomologies of GKM orbifolds and weighted Grassmann orbifolds" @default.
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