Abstract
We consider a planar surface $\Sigma$ of infinite type which has Thompson's group $\mathcal{T}$ as asymptotic mapping class group. We construct the asymptotic pants complex $\mathcal{C}$ of $\Sigma$ and prove that the group $\mathcal{T}$ acts transitively by automorphisms on it. Finally, we establish that the automorphism group of the complex $\mathcal{C}$ is an extension of the Thompson group $\mathcal{T}$ by $\mathbb{Z}/2\mathbb{Z}$
Citation
Ariadna Fossas. Maxime Nguyen. "Thompson's group $T$ is the orientation-preserving automorphism group of a cellular complex." Publ. Mat. 56 (2) 305 - 326, 2012.
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