Fernando Galaz-García fernando.galaz-garcia@durham.ac.uk
Associate Professor
Three-dimensional Alexandrov spaces: A survey
Galaz-García, Fernando; Núñez-Zimbrón, Jesús
Authors
Jesús Núñez-Zimbrón
Contributors
Gerardo Arizmendi Echegaray
Editor
Luis Hernández-Lamoneda
Editor
Rafael Herrera Guzmán
Editor
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.
Citation
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. https://doi.org/10.1007/978-3-030-99298-9_2
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 |
DOI | https://doi.org/10.1007/978-3-030-99298-9_2 |
Public URL | https://durham-repository.worktribe.com/output/1620966 |
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Copyright 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
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