2009/06/08 by Darryl McCullough, Kashyap Rajeevsarathy, McCullough, Darryl +1
Computer Science · Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GT #msc:57M99 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0906.1601
15 pages, 6 figures
arxiv created 2009/06/08 · arxiv updated 2009/12/01
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.