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Main Authors: Hirose, Susumu, Monden, Naoyuki
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2310.13272
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author Hirose, Susumu
Monden, Naoyuki
author_facet Hirose, Susumu
Monden, Naoyuki
contents Wajnryb proved that the mapping class group of a closed oriented surface is generated by two elements. We proved that the mapping class group is generated by two pseudo-Anosov elements. In particular, if the genus is greater than or equal to nine, we can take the generators to two conjugate pseudo-Anosov elements with arbitrarily large dilatations. Another result we prove is that the mapping class group is generated by two conjugate reducible but not periodic elements if the genus is greater than or equal to eight. We also give similar results to the first and third results for the hyperelliptic mapping class group when the genus is greater than or equal to one.
format Preprint
id arxiv_https___arxiv_org_abs_2310_13272
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On generating mapping class groups by pseudo-Anosov elements
Hirose, Susumu
Monden, Naoyuki
Geometric Topology
Wajnryb proved that the mapping class group of a closed oriented surface is generated by two elements. We proved that the mapping class group is generated by two pseudo-Anosov elements. In particular, if the genus is greater than or equal to nine, we can take the generators to two conjugate pseudo-Anosov elements with arbitrarily large dilatations. Another result we prove is that the mapping class group is generated by two conjugate reducible but not periodic elements if the genus is greater than or equal to eight. We also give similar results to the first and third results for the hyperelliptic mapping class group when the genus is greater than or equal to one.
title On generating mapping class groups by pseudo-Anosov elements
topic Geometric Topology
url https://arxiv.org/abs/2310.13272