Roots of Dehn twists on nonorientable surfaces
Abstract
Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable surface N_g of genus g. We explore the existence of roots and, following the work of McCullough, Rajeevsarathy and Monden, give a simple arithmetic description of their conjugacy classes. We also study roots of maximal degree and prove that if we fix an odd integer n>1, then for each sufficiently large g, t_c has a root of degree n in M(N_g). Moreover, for any possible degree n we provide explicit expressions for a particular type of roots of Dehn twists about nonseparating circles in N_g.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 DOI:
 10.48550/arXiv.1701.00531
 arXiv:
 arXiv:1701.00531
 Bibcode:
 2017arXiv170100531P
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  General Topology;
 Mathematics  Group Theory
 EPrint:
 A thoroughly revised version