Cohomogeneity one RCD spaces

Abstract: I will speak about joint work with Diego Corro and Jaime Santos in which we study RCD-spaces $(X,d,m)$ with group actions by isometries preserving the reference measure $m$ and whose orbit space has dimension one, i.e. cohomogeneity one actions. RCD spaces are metric measure spaces with a notion of "Ricci curvature bounded below and dimension bounded above". In the talk I will mention a version of the Slice Theorem for cohomogeneity one spaces that we show and then use to obtain topological structural results analogous to those available in the smooth setting. I will also mention how to construct new cohomogeneity one RCD-spaces. As an application of these results we obtain the classification of cohomogeneity one, "non-collapsed" RCD-spaces of dimension at most $4$.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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