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Sufficiently collapsed Alexandrov 3-spaces

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Fernando Galaz-Garcia
Universität Bonn/Karlsruhe Institute of Technology
Thu, 2018-06-21 16:30 - 17:30
MPIM Lecture Hall

In Riemannian geometry, collapse imposes strong geometric and topological restrictions on
the spaces on which it occurs. In the case of Alexandrov spaces, which generalize Riemannian manifolds with a lower sectional curvature bound, collapse is fairly well understood in dimension
three. In this talk I will discuss the topology of sufficiently collapsed Alexandrov 3-spaces: when
the space is irreducible, it is modeled on one of the eight three-dimensional dimensional Thurston geometries, excluding the hyperbolc one. This extends a result of Shioya and Yamaguchi, originally
formulated for Riemannian manifolds, to the Alexandrov setting. (Joint with Luis Guijarro and Jesús Núñez-Zimbrón).

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