Recognising perfect fits

TL;DR

This paper introduces an algorithm to determine if a pseudo-Anosov flow has perfect fits and whether two such flows without perfect fits are orbit equivalent, aiding classification of these flows.

Contribution

It provides the first algorithmic method to detect perfect fits in pseudo-Anosov flows and to decide orbit equivalence for flows without perfect fits.

Findings

Algorithm successfully detects perfect fits in given flows.

Algorithm determines orbit equivalence for flows without perfect fits.

Advances computational tools in the study of pseudo-Anosov flows.

Abstract

A pseudo-Anosov flow is said to have perfect fits if there are stable and unstable leaves that are asymptotic in the universal cover. We give an algorithm to decide, given a box decomposition of a pseudo-Anosov flow, if the flow has perfect fits. As a corollary, we obtain an algorithm to decide whether two flows without perfect fits are orbit equivalent.