Thompson’s group \(\mathcal T\) is the orientation-preserving automorphism group of a cellular complex. (English) Zbl 1292.57014

Summary: 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 \(\mathbb{Z}/2\mathbb{Z}\)


57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
20F38 Other groups related to topology or analysis
57M07 Topological methods in group theory
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
Full Text: DOI Euclid


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