# Three-dimensional Alexandrov spaces with local isometric circle actions

## TL;DR

This paper classifies three-dimensional Alexandrov spaces with local isometric circle actions, revealing their topological structure as connected sums of 3-manifolds and suspensions of the real projective plane.

## Contribution

It provides a topological and equivariant classification of such spaces, extending understanding of Alexandrov spaces with circle symmetries.

## Key findings

- Spaces are homeomorphic to connected sums of 3-manifolds with local circle actions
- Includes finitely many suspensions of the real projective plane
- Classifies spaces based on their topological and equivariant properties

## Abstract

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 homeomorphic to connected sums of some closed 3-manifold with a local circle action and finitely many copies of the suspension of the real projective plane.