JournalscmhVol. 97, No. 1pp. 1–59

Normal generators for mapping class groups are abundant

  • Justin Lanier

    University of Chicago, USA
  • Dan Margalit

    Georgia Institute of Technology, Atlanta, USA
Normal generators for mapping class groups are abundant cover
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Abstract

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 2\sqrt{2} 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. 1–59

DOI 10.4171/CMH/526