Mapping class groupoids and Thompson's groups

A. Muhammed Uludağ; Mustafa Topkara; Özge Ülkem; Ayberk Zeytin

Mapping class groupoids and Thompson's groups

Geometric Topology 2024-05-30 v4

Authors: A. Muhammed Uludağ , Mustafa Topkara , Özge Ülkem , Ayberk Zeytin

Abstract

We introduce a groupoid ${\mathbf{\Pi MG}}}$ , called the fundamental modular groupoid, which is a variant of Penner's mapping class groupoid. We study how it relates to the surface mapping class groups and Thompson's group $\mathsf T$ . We also introduce larger groupoid $\mathbf{\Omega MG}$ , which is related to outer automorphisms of free groups and Thompson's group $\mathsf V$ in a similar manner.

Keywords

mapping class groups mapping class groups of surfaces automorphism groups

Cite

@article{arxiv.1807.08788,
  title  = {Mapping class groupoids and Thompson's groups},
  author = {A. Muhammed Uludağ and Mustafa Topkara and Özge Ülkem and Ayberk Zeytin},
  journal= {arXiv preprint arXiv:1807.08788},
  year   = {2024}
}

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43 pages, 24 figures

Mapping class groupoids and Thompson's groups

Abstract

Keywords

Cite

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