Moves on Filtered PL Manifolds and Stratified PL Spaces

TL;DR

This paper extends classical results to provide finite moves connecting triangulations of filtered PL manifolds and stratified spaces, accommodating local models for neighborhoods of strata.

Contribution

It introduces a set of finite moves for triangulations of filtered PL manifolds and stratified spaces, generalizing previous results to more complex local structures.

Findings

Finite sets of moves relate triangulations respecting filtrations.

Extension of Pachner and Casali's results to stratified spaces.

Applicable to neighborhoods modeled by simple local structures.

Abstract

We extend results of Pachner and Casali to give finite sets of moves relating triangulations of PL manifolds respecting filtrations by locally flat manifolds and stratifications in which a finite family of simple local models exists for neighborhoods of strata.