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Endperiodic maps,
splitting sequences, and branched surfaces
Michael P Landry and Chi Cheuk Tsang |
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Geometry & Topology 29 (2025) 4531–4663
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DOI: 10.2140/gt.2025.29.4531
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Abstract |
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We strengthen the unpublished theorem of Gabai and Mosher that every depth one sutured manifold contains a very full dynamic branched surface by showing that the branched surface can be chosen to satisfy an additional property we call veering. To this end we prove that every endperiodic map admits a periodic splitting sequence of train tracks carrying its positive Handel–Miller lamination. This completes step one of Gabai and Mosher’s unpublished two-step proof that every taut finite-depth foliation of a compact, oriented, atoroidal 3-manifold is almost transverse to a pseudo-Anosov flow. Further, a veering branched surface in a sutured manifold is a generalization of a veering triangulation, and we extend some of the theory of veering triangulations to this setting. In particular we show that the branched surfaces we construct are unique up to a natural equivalence relation, and give an algorithmic way to compute the foliation cones of Cantwell and Conlon. |
Keywords
endperiodic map, pseudo-Anosov flow, sutured manifold,
train track splitting sequence, veering branched surface
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Mathematical Subject Classification
Primary: 37E30, 57K32
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References |
Publication
Received: 18 May 2023
Revised: 2 August 2024
Accepted: 7 September 2024
Published: 31 December 2025
Proposed: Mladen Bestvina
Seconded: Cameron Gordon, Dmitri Burago
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Authors |
| Michael P Landry | |
| Department of Mathematics and
Statistics Saint Louis University St Louis, MO United States |
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| Chi Cheuk Tsang | |
| Department of Mathematics University of California, Berkeley Berkeley, CA United States |
Département de mathématiques Université du Québec à Montréal Montréal, QC Canada |
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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