Collapsing three-dimensional closed Alexandrov spaces with a lower curvature bound

TL;DR

This paper classifies the topologies of three-dimensional closed Alexandrov spaces with lower curvature bounds that converge to lower-dimensional spaces in the Gromov-Hausdorff sense.

Contribution

It provides a topological classification of 3D closed Alexandrov spaces under Gromov-Hausdorff convergence with curvature bounds, extending understanding of their geometric limits.

Findings

Classified topologies of 3D Alexandrov spaces under convergence.

Identified possible limit spaces in Gromov-Hausdorff topology.

Extended the theory of Alexandrov spaces with curvature bounds.

Abstract

In the present paper, we determine the topologies of three-dimensional closed Alexandrov spaces which converge to lower dimensional spaces in the Gromov-Hausdorff topology.