caa a22 4500 445884207 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9541-4 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9541-4 Roots of Dehn twists [Elektronische Daten] [Darryl McCullough, Kashyap Rajeevsarathy] Margalit and Schleimer found examples of roots of the Dehn twist t C about a nonseparating curve C in a closed orientable surface, that is, homeomorphisms h such that h n=t C in the mapping class group. Our main theorem gives elementary number-theoretic conditions that describe the n for which an n th root of t C 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,n th roots exist for all genera greater than (n − 2)(n − 1)/2. We also describe all n th roots having n greater than or equal to the genus. Springer Science+Business Media B.V., 2010 Surface nationallicence Mapping class nationallicence Dehn twist nationallicence Nonseparating nationallicence Curve nationallicence Root nationallicence McCullough Darryl Department of Mathematics, University of Oklahoma, 73019, Norman, OK, USA aut Rajeevsarathy Kashyap Department of Mathematics, University of Oklahoma, 73019, Norman, OK, USA aut Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 397-409 0046-5755 151:1<397 2011 151 10711 https://doi.org/10.1007/s10711-010-9541-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9541-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- McCullough Darryl Department of Mathematics, University of Oklahoma, 73019, Norman, OK, USA aut NATIONALLICENCE 700 1- Rajeevsarathy Kashyap Department of Mathematics, University of Oklahoma, 73019, Norman, OK, USA aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 397-409 0046-5755 151:1<397 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer