On Limit Amalgamations of Stratififed Spaces

TL;DR

This paper demonstrates that stratified spaces and related geometric classes possess categorical Fraïssé properties, introduces a new example of a stratified pseudomanifold with finite oscillation, and explores implications for geometry and logic.

Contribution

It establishes the Fraïssé properties of stratified spaces and provides a novel example satisfying finite oscillation under smooth stratified actions.

Findings

Stratified spaces satisfy categorical Fraïssé properties.

A new stratified pseudomanifold example with finite oscillation is presented.

The work links geometric structures with logical properties.

Abstract

In this article we prove that stratified spaces and other geometric subfamilies satisfy categorical Fra\"iss\'e properties, a matter that might be of interest for both geometers and logicians. As a motivation we show a new example of a stratified pseudomanifold that satisfies the finite oscillation property with respect to a smooth stratified action. Part of this work was presented by the authors at the First Meeting of Logic and Geometry in Bogot\'a, on Sept. 2010.