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Peer-reviewedCC BYGeometry & Topology

Endperiodic maps via pseudo-Anosov flows

  • Michael P. Landry1
  • Yair N. Minsky2
  • Samuel J. Taylor3
  1. 1Department 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
  2. 2Department of Mathematics, Yale University, New Haven, CT, United States
  3. 3Department of Mathematics, Temple University, Philadelphia, PA, United States
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@article{landry2026endperiodic,
  title = {{Endperiodic maps via pseudo-Anosov flows}},
  author = {Michael P. Landry and Yair N. Minsky and Samuel J. Taylor},
  journal = {Geometry \& Topology},
  year = {2026},
  month = jul,
  doi = {10.2140/gt.2026.30.1987},
  url = {https://doi.org/10.2140/gt.2026.30.1987},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Endperiodic maps via pseudo-Anosov flows
AU  - Michael P. Landry
AU  - Yair N. Minsky
AU  - Samuel J. Taylor
PY  - 2026
DA  - 2026/07/18
JO  - Geometry & Topology
DO  - 10.2140/gt.2026.30.1987
UR  - https://doi.org/10.2140/gt.2026.30.1987
AB  - 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.
SN  - 1364-0380
SN  - 1465-3060
ER  -