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Endperiodic maps via
pseudo-Anosov flows
Michael P Landry, Yair N Minsky and Samuel J Taylor |
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Geometry & Topology 30 (2026) 1987–2042
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Abstract |
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We show that every atoroidal endperiodic map of an infinite-type surface can be obtained from a depth-one foliation in a fibered hyperbolic 3-manifold, reversing a well-known construction of Thurston. This can be done almost-transversely to the canonical suspension flow, and as a consequence we recover the Handel–Miller laminations of such a map directly from the fibered structure. We also generalize from the finite-genus case the relation between topological entropy, growth rates of periodic points, and growth rates of intersection numbers of curves. Fixing the manifold and varying the depth-one foliations, we obtain a description of the Cantwell–Conlon foliation cones and a proof that the entropy function on these cones is continuous and convex. |
Keywords
endperiodic, pseudo-Anosov
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Mathematical Subject Classification
Primary: 57K20, 57K32
Secondary: 37C35, 37C86
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References |
Publication
Received: 25 April 2025
Revised: 26 August 2025
Accepted: 5 November 2025
Published: 18 July 2026
Proposed: David Gabai
Seconded: Benson Farb, Ian Agol
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Authors |
| Michael P Landry | |
| Department of Mathematics Washington University in Saint Louis St. Louis, MO United States |
Department of Mathematics and
Statistics Saint Louis University St. Louis, MO United States |
| Yair N Minsky | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Samuel J Taylor | |
| Department of Mathematics Temple University Philadelphia, PA United States |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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