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.
Abstract
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) |
| Status: | Peer-reviewed |
| 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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