Torus actions on 4-dimensional Alexandrov spaces

Abstract: Equivariant classification of $T^2$-actions on smooth closed orientable 4-dimensional manifolds was obtained by Orlik and Raymond in 70's. In particular, they showed that the smooth classification is equivalent to the topological classification. In this talk, I present an equivariant classification of isometric $T^2$-actions on closed, orientable, four-dimensional Alexandrov spaces, which generalizes the equivariant classification of Orlik and Raymond. Moreover, we show that such Alexandrov spaces are equivariantly homeomorphic to 4-dimensional Riemannian orbifolds with isometric $T^2$-actions. This is joint work with Diego Corro and Jesús Núñez-Zimbrón.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

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

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.

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