Roots of Dehn twists on nonorientable surfaces

Anna Parlak , Michał Stukow


Margalit 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.
Author Anna Parlak
Anna Parlak,,
, Michał Stukow (FMPI / IM)
Michał Stukow,,
- Institute of Mathematics
Journal seriesJournal of Knot Theory and its Ramifications, ISSN 0218-2165, e-ISSN 1793-6527, (N/A 70 pkt)
Issue year2019
Publication size in sheets1.5
Article number1950077
Keywords in Englishmapping class group, nonorientable surface, Dehn twist, roots
ASJC Classification2602 Algebra and Number Theory
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 06-03-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.783; WoS Impact Factor: 2018 = 0.461 (2) - 2018=0.516 (5)
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