Fecha y hora : Lunes, 9 de Noviembre de 2020, 4:30pm (en línea)

Por: Masoumeh Zarei, University of Augsburg, Alemania

Título: Equivariant cohomology of cohomogeneity one Alexandrov spaces

Resumen: Equivariant cohomology of a G-space is defined as the cohomology of the Borel construction $X_G:= X\times_{G}EG$. The action of G isi called Cohen-Macaulay if the Krull dimension of the equivariant cohomology $H^*(X_G;\mathbb{Q})$ is equal to its depth as a $H^*(BG;\mathbb{Q})$-module. In this talk, I give a characterization of those Alexandrov spaces admitting a cohomogeneity one action of a compact connected Lie group G for which the action is Cohen–Macaulay. This generalizes a similar result for manifolds to the singular setting of Alexandrov spaces where, in contrast to the manifold case, we find several actions which are not Cohen–Macaulay. This is joint work with Manuel Amann.