{"title":"On integral Chang-Skjelbred computations with disconnected isotropy groups","authors":"Leopold Zoller","doi":"arxiv-2407.03052","DOIUrl":null,"url":null,"abstract":"The Chang-Skjelbred method computes the cohomology of a suitable space with a\ntorus action from its equivariant one-skeleton. We show that, under certain\nrestrictions on the cohomological torsion, the integral cohomology is encoded\nin the one-skeleton even in the presence of arbitrary disconnected isotropy\ngroups. We provide applications to Hamiltonian actions as well as to the GKM\ncase. In the latter, our results lead to a modification of the GKM formula for\ngraph cohomology.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.03052","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.