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arXiv · 2310.18412

Homoclinic leaves, Hausdorff limits and homeomorphisms

Ian Biringer·Cyril Lecuire
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Abstract

We show that except for one exceptional case, a lamination on the boundary of a 3-dimensional handlebody H is a Hausdorff limit of meridians if and only if it is commensurable to a lamination with a 'homoclinic leaf'. This is a precise version of a philosophy called Casson's Criterion, which appeared in unpublished notes of A. Casson. Applications include a characterization of when a non-minimal lamination is a Hausdorff limit of meridians, in terms of properties of its minimal components, and a related characterization of which reducible self-homeomorphisms of the boundary of H have powers that extend to subcompressionbodies of H.

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Ian Biringer, Cyril Lecuire. 2023-10-27. Homoclinic leaves, Hausdorff limits and homeomorphisms. https://doi.org/10.2140/agt.2026.26.1803

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