Puncture-Forgetting Maps for Measured Foliations and Applications in Teichmüller Space and Complex Dynamics
Year: 2026
Type: preprint
Abstract: We introduce puncture-forgetting maps for measured foliations and investigate their relations with mapping class groups, Teichmüller spaces, and extremal length. To this end, we develop the notions of cube complexes of pre-homotopic multicurves and tree coordinate systems on CAT(0) cube complexes. As an application to the dynamics of post-critically finite rational maps on the Riemann sphere, we obtain a partial result toward the finite curve attractor conjecture posed by Kevin Pilgrim. We also apply these methods to uncover a relation between horospheres and geodesic flows in the universal curve over Teichmüller space.
Source: arXiv (Cornell University)
Authors: Kahn, Jeremy, Park, Insung
Institutions: Brown University, Stony Brook School, Stony Brook University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171950674