单纯GKM轨形复形的整等变K-理论与配边环
Integral equivariant $K$-theory and cobordism ring of simplicial GKM orbifold complexes
AI总结：
本文定义了单纯GKM轨形复形，引入了可构建与可分性质，并计算了可分单纯GKM轨形复形的整等变上同调环、等变K-理论环及等变配边环。
摘要：
本文定义了“simplicial GKM orbifold complexes”并研究了它们的一些拓扑性质。我们引入了正则图的过滤和“simplicial graph complexes”的概念，它们与simplicial GKM orbifold complexes密切相关。我们讨论了在simplicial GKM orbifold complex上确认不变$q$-CW复形结构的必要条件。我们引入了“buildable”和“divisive”的simplicial GKM orbifold complexes。我们证明了buildable simplicial GKM orbifold complex是等变形式的，而divisive simplicial GKM orbifold complex是整等变形式的。我们给出了某些simplicial GKM orbifold complexes的整等变上同调环的组合描述。我们证明了轨形$G$-向量丛在带有有理系数的等变上同调和等变$K$-理论下的Thom同构定理。我们将Harada-Henriques-Holm (2005)的主要结果扩展到了配备有“singular invariant stratification”的$G$-空间范畴。我们计算了divisive simplicial GKM orbifold complexes的整等变上同调环、等变$K$-理论环和等变配边环。我们描述了divisive simplicial GKM orbifold complex的整广义等变上同调的一个基。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
