Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric
Differential Geometry
2020-05-21 v2 Metric Geometry
Abstract
We prove that sufficiently collapsed, closed and irreducible three-dimensional Alexandrov spaces are modeled on one of the eight three-dimensional Thurston geometries. This extends a result of Shioya and Yamaguchi, originally formulated for Riemannian manifolds, to the Alexandrov setting.
Keywords
Cite
@article{arxiv.1709.02336,
title = {Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric},
author = {Fernando Galaz-Garcia and Luis Guijarro and Jesús Núñez-Zimbrón},
journal= {arXiv preprint arXiv:1709.02336},
year = {2020}
}
Comments
We have added a proof of the fact that a closed collapsing Alexandrov 3-space cannot admit hyperbolic geometry (see Remark B). This improves our main Theorem (Theorem A) by ruling out the appearance of hyperbolic geometry. 24 pages, 3 Tables