Roots of Dehn twists on nonorientable surfaces

Anna Parlak , Michał Stukow

Abstract

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
Vol28
No12
Pages1-31
Publication size in sheets1.5
Article number1950077
Keywords in Englishmapping class group, nonorientable surface, Dehn twist, roots
ASJC Classification2602 Algebra and Number Theory
DOIDOI:10.1142/S0218216519500779
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)
Citation count*
Cite
Share Share

Get link to the record


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back
Confirmation
Are you sure?