On the automorphism group of the asymptotic pants complex of a planar surface of infinite type
Ariadna Fossas (IF), Maxime Nguyen (IF)
TL;DR
This paper studies the automorphism group of the asymptotic pants complex of an infinite-type planar surface, revealing its structure as an extension of the Thompson group T by Z/2Z.
Contribution
It constructs the asymptotic pants complex for an infinite-type surface with Thompson group T as the asymptotic mapping class group and determines its automorphism group.
Findings
Thompson group T acts transitively on the complex
Automorphism group of the complex is an extension of T by Z/2Z
The complex provides new insights into the symmetries of infinite-type surfaces
Abstract
We consider a planar surface \Sigma of infinite type which has the Thompson group T as asymptotic mapping class group. We construct the asymptotic pants complex C of \Sigma and prove that the group T acts transitively by automorphisms on it. Finally, we establish that the automorphism group of the complex C is an extension of the Thompson group T by Z/2Z.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology