A note on the rigidity of unmeasured lamination spaces (Q2855917)

Let \(S\) be an orientable surface of finite type which is not a sphere with at most four punctures, a torus with at most two punctures, nor a closed surface of genus 2, and let \({\mathcal UML}(S)\) be the space of unmeasured laminations endowed with the quotient topology from the measured lamination space with the Thurston topology. The author proves that every homeomorphism \(f : {\mathcal UML}(C) \rightarrow {\mathcal UML}(S)\) is induced by an unique element of the extended mapping class group. The proof relies upon a result of \textit{A. Papadopoulos} [Proc. Am. Math. Soc. 136, No. 12, 4453--4460 (2008; Zbl 1154.57017)].