On generating mapping class groups by pseudo-Anosov elements
arXiv:2310.13272
Abstract
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.
18 pages, 5 figures, we corrected some minor typos and changed some expressions. We added the proof of the latter part of Lemma 2.5 for genus greater than or equal to three