Generating Extended Mapping Class Groups with Two Periodic Elements
Abstract
The extended mapping class group of a surface is defined to be the group of isotopy classes of (not necessarily orientation-preserving) homeomorphisms of . 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=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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