Dynamics of veering triangulations: infinitesimal components of their flow graphs and applications

Agol, Ian; Tsang, Chi Cheuk

doi:10.2140/agt.2024.24.3401

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Dynamics of veering triangulations: infinitesimal components of their flow graphs and applications

Ian Agol and Chi Cheuk Tsang

Algebraic & Geometric Topology 24 (2024) 3401–3453

DOI: 10.2140/agt.2024.24.3401

Abstract

We study the strongly connected components of the flow graph associated to a veering triangulation, and show that the infinitesimal components must be of a certain form, which have to do with subsets of the triangulation which we call “walls”. We show two applications of this knowledge: first, we fix a proof in the original paper by the first author which introduced veering triangulations; and second, give an alternate proof that veering triangulations induce pseudo-Anosov flows without perfect fits, which was initially proved by Schleimer and Segerman.

Keywords

veering triangulation, flow graph, infinitesimal component, dilatation, pseudo-Anosov flow

Mathematical Subject Classification

Primary: 57M50

Secondary: 37D20, 37E30

References

Publication

Received: 24 January 2022

Revised: 9 November 2022

Accepted: 2 January 2023

Published: 7 October 2024

Authors

Ian Agol
Department of Mathematics University of California, Berkeley Berkeley, CA United States

Chi Cheuk Tsang
Département de mathématiques Université du Québec à Montréal Montreal, QC Canada

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