Three-dimensional Alexandrov spaces: A survey

Galaz-García, Fernando; Núñez-Zimbrón, Jesús

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