Geometry and Topology of collapsed three-dimensional Alexandrov Spaces
Fernando Galaz-García (Durham University)
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
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.
Organizers: | Fernando Galaz-García*, Carolyn Gordon, Ramiro Lafuente*, Emilio Lauret* |
*contact for this listing |