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- W4321473280 abstract "In this paper, we define `simplicial GKM orbifold complexes' and study some of their topological properties. We introduce the concept of filtration of regular graphs and `simplicial graph complexes', which have close relations with simplicial GKM orbifold complexes. We discuss the necessary conditions to confirm an invariant $q$-CW complex structure on a simplicial GKM orbifold complex. We introduce `buildable' and `divisive' simplicial GKM orbifold complexes. We show that a buildable simplicial GKM orbifold complex is equivariantly formal, and a divisive simplicial GKM orbifold complex is integrally equivariantly formal. We give a combinatorial description of the integral equivariant cohomology ring of certain simplicial GKM orbifold complexes. We prove the Thom isomorphism theorem for orbifold $G$-vector bundles for equivariant cohomology and equivariant $K$-theory with rational coefficients. We extend the main result of Harada-Henriques-Holm (2005) to the category of $G$-spaces equipped with `singular invariant stratification'. We compute the integral equivariant cohomology ring, equivariant $K$-theory ring and equivariant cobordism ring of divisive simplicial GKM orbifold complexes. We describe a basis of the integral generalized equivariant cohomology of a divisive simplicial GKM orbifold complex." @default.
- W4321473280 created "2023-02-23" @default.
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- W4321473280 date "2023-02-19" @default.
- W4321473280 modified "2023-10-17" @default.
- W4321473280 title "Integral equivariant $K$-theory and cobordism ring of simplicial GKM orbifold complexes" @default.
- W4321473280 doi "https://doi.org/10.48550/arxiv.2302.09581" @default.
- W4321473280 hasPublicationYear "2023" @default.
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