Towards the boundary of the fine curve graph
Abstract The fine curve graph was introduced as a geometric tool to study homeomorphisms of surfaces. In this paper, we study the Gromov boundary of this space and the local topology near points associated with certain foliations and laminations. We then give several applications including finding dynamically explicit elements with positive stable commutator length, and proving a Tits alternative for subgroups of containing a pseudo‐Anosov map, generalising a result of Hurtado–Xue.
Authors
- Sebastian Hensel (ORCID: https://orcid.org/0000-0002-9369-4173)
- Jonathan Bowden (ORCID: https://orcid.org/0000-0003-4008-9030)
- Richard Webb (ORCID: https://orcid.org/0000-0001-9161-0928)
Institutions
- Leibniz University Hannover (DE)
- University of Manchester (GB)
- Leibniz University of Applied Sciences (DE)
- L3S Research Center (DE)
Publication Details
- Journal
- Journal of Topology
- Published
- 2026-05-12
- DOI
- https://doi.org/10.1112/topo.70074
- Primary Topic
- Computational Geometry and Mesh Generation
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Engineering and Physical Sciences Research Council