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 o… ▽ More

Submitted 22 September, 2026; v1 submitted 29 July, 2026; originally announced July 2026.

Comments: 71 pages, 15 figures

MSC Class: 30F60; 57K20; 37F10

https://arxiv.org/abs/2607.27552