We provide a simple criterion for an element of the mapping class group of a closed surface to be a normal generator for the mapping class group. We apply this to show that every nontrivial periodic mapping class that is not a hyperelliptic involution is a normal generator for the mapping class group when the genus is at least 3. We also give many examples of pseudo-Anosov normal generators, answering a question of D. D. Long. In fact we show that every pseudo-Anosov mapping class with stretch factor less than is a normal generator. Even more, we give pseudo-Anosov normal generators with arbitrarily large stretch factors and arbitrarily large translation lengths on the curve graph, disproving a conjecture of Ivanov.
Cite this article
Justin Lanier, Dan Margalit, Normal generators for mapping class groups are abundant. Comment. Math. Helv. 97 (2022), no. 1, pp. 1–59DOI 10.4171/CMH/526