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Puncture-Forgetting Maps for Measured Foliations and Applications in Teichmüller Space and Complex Dynamics
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.
Related
- Complete classification of algebraically primitive Teichmüller curves in Ωℳg(g−1,g−1)hyp
- Algebraically primitive Teichmüller curves in Ω\mathcal M_g(2g-2)^{\mathrm{hyp}}
- Totally Geodesic Submanifolds of Teichmüller Space in Complex Dimension at Least Three
- Super Teichmüller Space
- Local convexity obstructions for bounded realizations of Teichmüller space
BibTeX
@misc{kahn2026punctureforgetting,
title = {{Puncture-Forgetting Maps for Measured Foliations and Applications in Teichmüller Space and Complex Dynamics}},
author = {Jeremy Kahn and Insung Park},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.27552},
eprint = {2607.27552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.27552},
}
RIS
TY - UNPB
TI - Puncture-Forgetting Maps for Measured Foliations and Applications in Teichmüller Space and Complex Dynamics
AU - Jeremy Kahn
AU - Insung Park
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2607.27552
UR - https://arxiv.org/abs/2607.27552
AB - 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.
ER -