Homoclinic leaves, Hausdorff limits and homeomorphisms
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 This is a precise version of a philosophy called Casson's Criterion, which appeared in unpublished notes of A. Casson.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 ∂H have powers that extend to subcompressionbodies of H.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
Advanced Numerical Analysis Techniques
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 5
- Pages
- 1803–1868
- Publication date
- 15 May 2026
- Language
- EN