关于带断开各向同性群的张-斯凯尔布雷德积分计算

arXiv - MATH - Algebraic Topology Pub Date : 2024-07-03 DOI:arxiv-2407.03052

Leopold Zoller

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引用次数: 0

摘要

Chang-Skjelbred 方法通过等变单骨架计算具有atorus 作用的合适空间的同调。我们证明，在同调扭转的某些限制条件下，即使存在任意断开的各向同性群，积分同调也会被编码在单骨架中。我们提供了哈密顿作用和 GKM 案例的应用。在后者中，我们的结果导致了对 GKM 公式图同调的修改。

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On integral Chang-Skjelbred computations with disconnected isotropy groups

The Chang-Skjelbred method computes the cohomology of a suitable space with a torus action from its equivariant one-skeleton. We show that, under certain restrictions on the cohomological torsion, the integral cohomology is encoded in the one-skeleton even in the presence of arbitrary disconnected isotropy groups. We provide applications to Hamiltonian actions as well as to the GKM case. In the latter, our results lead to a modification of the GKM formula for graph cohomology.

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arXiv - MATH - Algebraic Topology

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