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Three-dimensional Alexandrov spaces: A survey

Galaz-García, Fernando and Núñez-Zimbrón, Jesús (2022) 'Three-dimensional Alexandrov spaces: A survey.', in Recent Advances in Alexandrov Geometry. , pp. 49-88. CIMAT Lectures in Mathematical Sciences.


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.

Item Type:Book chapter
Full text:Publisher-imposed embargo until 25 July 2023.
(AM) Accepted Manuscript
File format - PDF
Publisher Web site:
Publisher statement:This a post-peer-review, pre-copyedit version of a chapter published in CIMAT Lectures in Mathematical Sciences. The final authenticated version is available online at:
Date accepted:No date available
Date deposited:27 September 2022
Date of first online publication:25 July 2022
Date first made open access:25 July 2023

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