Homoclinic leaves, Hausdorff limits and homeomorphisms

Biringer, Ian; Lecuire, Cyril

doi:10.2140/agt.2026.26.1803

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Homoclinic leaves, Hausdorff limits and homeomorphisms

Ian Biringer and Cyril Lecuire

Algebraic & Geometric Topology 26 (2026) 1803–1868

DOI: 10.2140/agt.2026.26.1803

Abstract

We show that except for one exceptional case, a lamination on the boundary of a handlebody $H$ is commensurable to a Hausdorff limit of meridians if and only if it is commensurable to a lamination with a “homoclinic leaf”. This is an “if and only if” version of a theorem called Casson’s criterion. Applications of our techniques include a characterisation of when a nonminimal lamination is a Hausdorff limit of meridians, in terms of properties of its minimal components, and a related characterisation of which reducible self-homeomorphisms of $\partial H$ have powers that extend to subcompression bodies of $H$ .

Keywords

handlebody, meridian, lamination, homoclinic leaf, Casson's criterion, homeomorphism, extension

Mathematical Subject Classification

Primary: 57K30, 57K32

References

Publication

Received: 6 June 2024

Revised: 16 February 2025

Accepted: 29 May 2025

Published: 15 May 2026

Authors

Ian Biringer
Department of Mathematics Boston College Chestnut Hill, MA United States

Cyril Lecuire
ENS de Lyon site Monod UMPA UMR 5669 CNRS Lyon France

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Volume 26, issue 5 (2026)