Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Harris, Reid
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403623442