Geometry and Topology of collapsed three-dimensional Alexandrov Spaces

Fernando Galaz-García (Durham University)

21-Apr-2021, 16:00-17:00 (3 years ago)

Abstract: In Riemannian geometry, collapse imposes strong geometric and topological restrictions on the spaces on which it occurs. In the case of Alexandrov spaces, which are metric generalizations of complete Riemannian manifolds with a uniform lower sectional curvature bound, collapse is fairly well understood in dimension three. In this talk, I will discuss the geometry and topology of three-dimensional Alexandrov spaces and focus on those which are sufficiently collapsed. When such spaces are irreducible, they are modeled on one of the eight three-dimensional dimensional Thurston geometries, excluding the hyperbolic one. This extends a result of Shioya and Yamaguchi, originally formulated for Riemannian manifolds, to the Alexandrov setting. We will briefly discuss how spaces with circle actions enter the picture. (Joint work with Luis Guijarro and Jesús Núñez-Zimbrón).

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

( paper | video )


Virtual seminar on geometry with symmetries

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

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Organizers: Fernando Galaz-García*, Carolyn Gordon, Ramiro Lafuente*, Emilio Lauret*
*contact for this listing

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