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Three-dimensional Alexandrov spaces: A survey

Galaz-García, Fernando; Núñez-Zimbrón, Jesús

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Jesús Núñez-Zimbrón


Gerardo Arizmendi Echegaray

Luis Hernández-Lamoneda

Rafael Herrera Guzmán


We survey several results concerning the geometry and topology of threedimensional Alexandrov spaces with the aim of providing a panoramic and up-to-date view of the subject. In particular we present the classification of positively and nonnegatively curved spaces, the geometrization theorem, a discussion of known results for simply-connected and aspherical spaces, the equivariant and topological classifications of closed three-dimensional Alexandrov spaces with isometric compact Lie group actions, and recent developments on collapsing theory.


Galaz-García, F., & Núñez-Zimbrón, J. (2022). Three-dimensional Alexandrov spaces: A survey. In G. Arizmendi Echegaray, L. Hernández-Lamoneda, & R. Herrera Guzmán (Eds.), Recent Advances in Alexandrov Geometry (49-88). Springer Verlag.

Online Publication Date Jul 25, 2022
Publication Date 2022
Deposit Date Sep 26, 2022
Publicly Available Date Jul 26, 2023
Publisher Springer Verlag
Pages 49-88
Series Title CIMAT Lectures in Mathematical Sciences
Book Title Recent Advances in Alexandrov Geometry
ISBN 978-3-030-99297-2
Public URL


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