# On three-dimensional Alexandrov spaces

@article{GalazGarca2013OnTA, title={On three-dimensional Alexandrov spaces}, author={Fernando Galaz‐Garc{\'i}a and Luis Guijarro}, journal={arXiv: Differential Geometry}, year={2013} }

We study three-dimensional Alexandrov spaces with a lower curvature bound, focusing on extending three classical results on three-dimensional manifolds: First, we show that a closed three-dimensional Alexandrov space of positive curvature, with at least one topological singularity, must be homeomorphic to the suspension of the real projective plane; we use this to classify, up to homeomorphism, closed, positively curved Alexandrov spaces of dimension three. Second, we classify closed three…

## 25 Citations

### Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature

- Mathematics
- 2016

We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the CD∗(K,N) sense, focusing our attention on those with positive or nonnegative Ricci curvature. First, we…

### Cohomogeneity one Alexandrov spaces in low dimensions

- MathematicsAnnals of Global Analysis and Geometry
- 2020

Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with…

### Cohomogeneity one Alexandrov spaces in low dimensions

- MathematicsAnnals of Global Analysis and Geometry
- 2020

Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with…

### Rigidity of actions on metric spaces close to three dimensional manifolds

- Mathematics
- 2022

. In this paper we propose a metric variation on the C 0 version of the Zimmer program for three manifolds. After a reexami-nation of the isometry groups of geometric three-manifolds, we consider…

### Finiteness and realization theorems for Alexandrov spaces with bounded curvature

- MathematicsBoletín de la Sociedad Matemática Mexicana
- 2019

Every closed Alexandrov space with a lower and upper curvature bound (in the triangle comparison sense) is a space of bounded curvature (in the sense of Berestovskii and Nikolaev). These spaces are…

### Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature

- MathematicsPotential Analysis
- 2017

We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the CD∗(K,N) sense, focusing our attention on those with positive or nonnegative Ricci curvature. First, we…

### Orientability and fundamental classes of Alexandrov spaces with applications

- Mathematics
- 2016

In the present paper, we consider several valid notions of orientability of Alexandov spaces and prove that all such conditions are equivalent. Further, we give topological and geometric applications…

### Three-dimensional Alexandrov spaces with local isometric circle actions

- Mathematics
- 2020

We obtain a topological and equivariant classification of closed, connected three-dimensional Alexandrov spaces admitting a local isometric circle action. We show, in particular, that such spaces are…

### Alexandrov spaces with maximal radius

- MathematicsGeometry & Topology
- 2022

Abstract. In this paper we prove several rigidity theorems related to and including Lytchak's problem. The focus is on Alexandrov spaces with \curv\geq1, nonempty boundary, and maximal radius…

### Riemannian Orbifolds with Non-Negative Curvature

- Mathematics
- 2014

RIEMANNIAN ORBIFOLDS WITH NON-NEGATIVE CURVATURE Dmytro Yeroshkin Wolfgang Ziller Recent years have seen an increase in the study of orbifolds in connection to Riemannian geometry. We connect this…

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