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Article Dans Une Revue Mathematical News / Mathematische Nachrichten Année : 2016

On the automorphisms group of the asymptotic pants complex of an infinite surface of genus zero

Louis Funar
Maxime Nguyen
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Résumé

The braided Thompson group $\mathcal B$ is an asymptotic mapping class group of a sphere punctured along the standard Cantor set, endowed with a rigid structure. Inspired from the case of finite type surfaces we consider a Hatcher-Thurston cell complex whose vertices are asymptotically trivial pants decompositions. We prove that the automorphism group $\hat{\mathcal B^{\frac{1}{2}}}$ of this complex is also an asymptotic mapping class group in a weaker sense. Moreover $\hat{\mathcal B^{\frac{1}{2}}}$ is obtained by $\mathcal B$ by first adding new elements called half-twists and further completing it.

Dates et versions

hal-01702788 , version 1 (07-02-2018)

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Citer

Louis Funar, Maxime Nguyen. On the automorphisms group of the asymptotic pants complex of an infinite surface of genus zero. Mathematical News / Mathematische Nachrichten, 2016, 289 (10), pp.1189-1207. ⟨hal-01702788⟩
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