Generating Extended Mapping Class Groups with Two Periodic Elements

2024/09/10 by Reid Harris, Harris, Reid
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2409.06350

openalex publication_date 2024/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The extended mapping class group of a surface Σ is defined to be the group of isotopy classes of (not necessarily orientation-preserving) homeomorphisms of Σ. We are able to show that the extended mapping class group of an n-punctured sphere is generated by two elements of finite order exactly when n\not=4. We use this result to prove that the extended mapping class group of a genus 2 surface is generated by two elements of finite order.

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• Generating the surface mapping class group by two elements
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• Generating the Mapping Class Group of a Nonorientable Surface by Two Elements or By Three Involutions
• Generators of the Mapping Class Group of a Nonorientable Punctured Surface