%0 Journal Article
%T Roots of Dehn twists
%A Darryl McCullough
%A Kashyap Rajeevsarathy
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0906.1601v1