Roots of Dehn twists

Darryl McCullough; Kashyap Rajeevsarathy

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arXiv · 0906.1601

Roots of Dehn twists

Darryl McCullough·Kashyap Rajeevsarathy

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Abstract

D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary number-theoretic conditions that describe the values of n for which an nth root exists, given the genus of the surface. Among its applications, we show that n must be odd, that the Margalit-Schleimer roots achieve the maximum value of n among the roots for a given genus, and that for a given odd n, nth roots exist for all genera greater than (n-2)(n-1)/2. We also describe all nth roots having n greater than or equal to the genus.

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BibTeX RIS

Darryl McCullough, Kashyap Rajeevsarathy. 2009-06-08. Roots of Dehn twists. https://arxiv.org/abs/0906.1601

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