# On topological rigidity of Alexandrov $3$-spaces

## TL;DR

This paper proves the Borel Conjecture for certain three-dimensional Alexandrov spaces, establishing topological rigidity results and exploring fundamental group characterizations and group actions.

## Contribution

It demonstrates the Borel Conjecture for closed, irreducible, and collapsed 3D Alexandrov spaces, advancing understanding of their topological rigidity.

## Key findings

- Proved the Borel Conjecture for specific 3D Alexandrov spaces
- Identified questions on fundamental groups and group actions on these spaces
- Discussed potential rigidity results and their implications

## Abstract

In this note we prove the Borel Conjecture for closed, irreducible and sufficiently collapsed three-dimensional Alexandrov spaces. We also pose several questions related to characterization of fundamental groups of three-dimensional Alexandrov spaces, finite groups acting on them and rigidity results.