Stability and equivariant Gromov--Hausdorff convergence

TL;DR

This paper explores the use of equivariant Gromov--Hausdorff convergence to establish stability results in Alexandrov spaces and introduces the concept of almost commutative diagrams to streamline proofs.

Contribution

It applies equivariant Gromov--Hausdorff convergence to prove stability in Alexandrov spaces and introduces almost commutative diagrams for simplified arguments.

Findings

Proved stability results for compact Alexandrov spaces.

Introduced almost commutative diagrams to simplify mathematical arguments.

Demonstrated applications of equivariant Gromov--Hausdorff convergence.

Abstract

We give applications of equivariant Gromov--Hausdorff convergence in various contexts. Namely, using equivariant Gromov--Hausdorff convergence, we prove a stability result in the setting of compact finite dimensional Alexandrov spaces. Moreover, we introduce the notion of an \emph{almost commutative diagram} and show that its use simplifies both exposition and argument.