Generating the Extended Mapping Class Group by Three Involutions

We prove that the extended mapping class group, $\rm Mod^{*}(\Sigma_{g})$, of a connected orientable surface of genus $g$, can be generated by three involutions for $g\geq 5$. In the presence of punctures, we prove that $\rm Mod^{*}(\Sigma_{g,p})$ can be generated by three involutions for $g\geq 10$...

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Hauptverfasser:	Altunoz, Tulin, Pamuk, Mehmetcik, Yildiz, Oguz
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Sprache:	eng
Schlagworte:	Mathematics - Geometric Topology
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creator	Altunoz, Tulin Pamuk, Mehmetcik Yildiz, Oguz
description	We prove that the extended mapping class group, $\rm Mod^{}(\Sigma_{g})$, of a connected orientable surface of genus $g$, can be generated by three involutions for $g\geq 5$. In the presence of punctures, we prove that $\rm Mod^{}(\Sigma_{g,p})$ can be generated by three involutions for $g\geq 10$ and $p\geq 6$ (with the exception that for $g\geq 11$, $p$ should be at least $15$).
doi_str_mv	10.48550/arxiv.2003.10907
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title	Generating the Extended Mapping Class Group by Three Involutions
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