Simultaneous flips on triangulated surfaces

TL;DR

This paper studies a new type of distance measure between triangulations of finite type surfaces, based on simultaneous flips, providing bounds that depend solely on the surface's topology.

Contribution

It introduces and analyzes a distance metric for triangulations using simultaneous flips, with bounds depending only on the surface's topology.

Findings

Upper bounds on the distance between triangulations

Distance depends only on surface topology

Analysis of simultaneous flips on triangulations

Abstract

We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds on distance between triangulations that only depend on the topology of the surface.