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<p>Wajnryb proved that the mapping class group of a closed oriented surface can be generated by two elements. In this paper we show that it can be generated by two pseudo-Anosov elements. In particular, if the genus is at least nine, the generators may be chosen to be two conjugate pseudo-Anosov elements with arbitrarily large dilatations. We also prove that, for genus at least eight, the mapping class group is generated by two conjugate reducible elements of infinite order. We also obtain analogous generation results by two pseudo-Anosov elements and by two conjugate reducible elements of infinite order for the hyperelliptic mapping class group.</p>

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On Generating Mapping Class Groups by Pseudo-Anosov Elements

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Susumu Hirose,
  • Naoyuki Monden

摘要

Wajnryb proved that the mapping class group of a closed oriented surface can be generated by two elements. In this paper we show that it can be generated by two pseudo-Anosov elements. In particular, if the genus is at least nine, the generators may be chosen to be two conjugate pseudo-Anosov elements with arbitrarily large dilatations. We also prove that, for genus at least eight, the mapping class group is generated by two conjugate reducible elements of infinite order. We also obtain analogous generation results by two pseudo-Anosov elements and by two conjugate reducible elements of infinite order for the hyperelliptic mapping class group.