Three-dimensional Alexandrov spaces: A survey

Galaz-García, Fernando; Núñez-Zimbrón, Jesús

doi:10.1007/978-3-030-99298-9_2

Three-dimensional Alexandrov spaces: A survey

Galaz-García, Fernando; Núñez-Zimbrón, Jesús

Authors

Professor Fernando Galaz Garcia fernando.galaz-garcia@durham.ac.uk
Associate Professor

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