Simultaneous Laminations

Isaac Broudy

geometric topology

Simultaneous Laminations

arXiv:2607.13676

summary

The paper analyzes the laminations Λ⁺_u and Λ⁻_u associated with universal circles of pseudo‑Anosov orbit spaces of taut foliations on atoroidal 3‑manifolds, showing they are determined by stable and unstable prelaminations and fit into a finite list of lamination pairs for the corresponding group actions on the circle.

Abstract

Calegari introduced the laminations $I^_{u}^{\pm}$ associated to a universal circle. We study the laminations $I^_{u}^{\pm}$ for pseudo-Anosov orbit space universal circles of taut foliations, on atoroidal three-manifolds. We prove that $I^_{u}^{+}$ and $I^_{u}^{-}$ are completely determined by the stable and unstable prelaminations on the boundary of the orbit space. Then, using a result of BarthelmÃ©, Bonatti, and Mann, we prove that for any action $I ¨ : I ¨ _{1} (M) \to Homeo^{+} (S^{1})$ coming from an orbit space of a pseudo-Anosov flow, there is a finite collection of lamination pairs such that $(I^_{u}^{+}, I^_{u}^{-})$ lies in this collection for any minimal orbit space universal circle whose action is conjugate to $I ¨ $ .

Topics & keywords

#laminations #universal circle #pseudo-Anosov flow #taut foliation #3-manifoldsΛ⁺_uΛ⁻_ustable prelaminationunstable prelaminationorbit spaceHomeo⁺(S¹)