On the involution generators of the mapping class group of a punctured surface

DOI10.1007/s00009-023-02439-6zbMath1527.57010arXiv2209.12382OpenAlexW4379881161MaRDI QIDQ6159763

Oğuz Yıldız, Mehmetcik Pamuk, Tülin Altunöz

Publication date: 20 June 2023

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.12382

zbMATH Keywords

generating setsinvolutionsmapping class groupspunctured surfaces

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Topological methods in group theory (57M07) Other groups related to topology or analysis (20F38) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

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• The mapping class group of a punctured surface is generated by three elements
• Generating the mapping class group of a punctured surface by involutions
• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• Involutions in surface mapping class groups
• Every mapping class group is generated by 6 involutions
• Mapping class group of a surface is generated by two elements
• Mapping class group is generated by three involutions
• Generating the extended mapping class group by three involutions
• The extended mapping class group can be generated by two torsions
• Generating the surface mapping class group by two elements
• Generating Symmetric Groups
• Generating the twist subgroup by involutions
• A finite presentation of the mapping class group of a punctured surface

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