Agol cycles of pseudo-Anosov 3-braids

TL;DR

This paper investigates the conditions under which Agol cycles serve as complete invariants for conjugacy classes of pseudo-Anosov 3-braids, providing insights into their equivalence and classification.

Contribution

It establishes necessary and sufficient conditions for the equivalence of Agol cycles in pseudo-Anosov 3-braids, advancing the understanding of their conjugacy invariants.

Findings

Identifies criteria for Agol cycle equivalence

Provides a classification framework for pseudo-Anosov 3-braids

Enhances understanding of conjugacy invariants in braid theory

Abstract

An Agol cycle is a complete invariant of the conjugacy class of a pseudo-Anosov mapping class. We study necessary and sufficient conditions for equivalent Agol cycles of pseudo-Anosov 3-braids.