Rigidity theorems for glued spaces being suspensions, cones and joins in Alexandrov geometry with curvature bounded below

TL;DR

This paper establishes rigidity theorems for glued Alexandrov spaces with curvature bounds, characterizing when such spaces form suspensions, cones, or joins, and explores properties of joins in the appendix.

Contribution

It provides new rigidity results for glued Alexandrov spaces and details properties of joins, advancing understanding of their geometric structure.

Findings

Rigidity theorems for glued spaces as suspensions, cones, or joins.

Basic properties of joins in Alexandrov geometry.

Conditions under which glued spaces form specific geometric structures.

Abstract

In the paper, we give rigidity theorems when the glued space of two Alexandrov spapces with curvature bounded below is a suspension, cone or join. And we list some basic properties of joins in Appendix.