Roots of Dehn twists on nonorientable surfaces
Anna Parlak , Michał Stukow
AbstractMargalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist tc about a nonseparating circle c in the mapping class group M(Ng) of a nonorientable surface Ng 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, tc has a root of degree n in M(Ng). Moreover, for any possible degree n, we provide explicit expressions for a particular type of roots of Dehn twists about nonseparating circles in Ng.
|Journal series||Journal of Knot Theory and its Ramifications, ISSN 0218-2165, e-ISSN 1793-6527, (N/A 70 pkt)|
|Publication size in sheets||1.5|
|Keywords in English||mapping class group, nonorientable surface, Dehn twist, roots|
|Score||= 70.0, 06-03-2020, ArticleFromJournal|
|Publication indicators||: 2018 = 0.783; : 2018 = 0.461 (2) - 2018=0.516 (5)|
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