Stabilisation of geometric directional bundle for a subanalytic set

TL;DR

This paper proves that the geometric directional bundle stabilizes for subanalytic sets, establishing it as a new invariant for analyzing the geometry of singular spaces.

Contribution

It demonstrates the stabilization of the geometric directional bundle specifically for subanalytic sets, advancing the understanding of invariants in singular space analysis.

Findings

Geometric directional bundle stabilizes for subanalytic sets.

Provides a new invariant for subanalytic singular spaces.

Answers the stabilization question positively for this class.

Abstract

In a previous paper we have introduced the notion of geometric directional bundle of a singular space, in order to introduce global bi-Lipschitz invariants. Then we have posed the question of whether or not the geometric directional bundle is stabilised as an operation acting on singular spaces. In this paper we give a positive answer in the case where the singular spaces are subanalytic sets, thus providing a new invariant associated with the subanalytic sets.