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 (530Kb)
|Publisher Web site:||https://doi.org/10.1007/978-3-030-99298-9_2|
|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: https://doi.org/10.1007/978-3-030-99298-9_2|
|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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