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<p>We provide a criterion for Alexandrov spaces to admit a Cohen–Macaulay cohomogeneity one action of a compact connected Lie group <i>G</i>. This generalizes an analogous result for manifolds, where no additional assumptions are considered, to the singular setting of Alexandrov spaces with the further assumption that classifying spaces of isotropy groups are “Sullivan spaces”. In contrast to the manifold case, we find several actions which are not Cohen–Macaulay. In fact, we present our results in a slightly more general context. We extend the methods in this field by a conceptual approach on equivariant cohomology via rational homotopy theory using an explicit rational model for a double mapping cylinder.</p>

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On the equivariant cohomology of cohomogeneity one Alexandrov spaces

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Manuel Amann,
  • Masoumeh Zarei

摘要

We provide a criterion for Alexandrov spaces to admit a Cohen–Macaulay cohomogeneity one action of a compact connected Lie group G. This generalizes an analogous result for manifolds, where no additional assumptions are considered, to the singular setting of Alexandrov spaces with the further assumption that classifying spaces of isotropy groups are “Sullivan spaces”. In contrast to the manifold case, we find several actions which are not Cohen–Macaulay. In fact, we present our results in a slightly more general context. We extend the methods in this field by a conceptual approach on equivariant cohomology via rational homotopy theory using an explicit rational model for a double mapping cylinder.