Equivariant cohomology of cohomogeneity-one actions: The topological case

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• 作者：Oliver Goertsches^a ; ^{goertsch@mathematik.uni-marburg.de} ; Augustin-Liviu Mare^b ; ^{mareal@math.uregina.ca}
• 关键词：Compact Lie groups ; Cohomogeneity one group actions on topological manifolds ; Equivariant cohomology ; Cohen&ndash ; Macaulay rings
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：218
• 期：Complete
• 页码：93-96
• 全文大小：224 K
• 卷排序：218

文摘

We show that for any cohomogeneity-one continuous action of a compact connected Lie group G   on a closed topological manifold the equivariant cohomology equipped with its canonical H⁎(BG)H⁎(BG)-module structure is Cohen–Macaulay. The proof relies on the structure theorem for these actions recently obtained by Galaz-García and Zarei. We generalize in this way our previous result concerning smooth actions.