Rocky Mountain Journal of Mathematics

On roots of Dehn twists

Naoyuki Monden

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Margalit and Schleimer \cite{MS} discovered a nontrivial root of the Dehn twist about a nonseparating curve on a closed oriented connected surface. We give a complete set of conjugacy invariants for such a root by using a classification theorem of Matsumoto and Montesinos \cite{MM1, MM2} for pseudo-periodic maps of negative twists. As an application, we determine the range of degree for roots of a Dehn twist.

Article information

Rocky Mountain J. Math., Volume 44, Number 3 (2014), 987-1001.

First available in Project Euclid: 28 September 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Monden, Naoyuki. On roots of Dehn twists. Rocky Mountain J. Math. 44 (2014), no. 3, 987--1001. doi:10.1216/RMJ-2014-44-3-987.

Export citation


  • L. Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), 73–98.
  • S. Gervais, A finite presentation of the mapping class group of a punctured surface, Topology 40 (2001), 703–725.
  • J. Gilman, On the Nielsen type and the classification for the mapping class group, Adv. Math. 40 (1981), 68–96.
  • D. Margalit and S. Schleimer, Dehn twists have roots, Geom. Topol. 13 (2009), 1495–1497.
  • Y. Matsumoto and J.M. Montesinos-Amilibia, Pseudo-periodic maps and degenerations of Riemann surfaces, Lect. Notes Math. 2030, Springer-Verlag, Heidelberg, 2011.
  • ––––, Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces, Bull. Amer. Math. Soc. 30 (1994), 70–75.
  • D. McCullough and K. Rajeevsarathy, Roots of Dehn twists, Geom. Ded. 151 (2011), 397–409.
  • J. Nielsen, Die Struktur periodischer Transformationen von Flächen, Danske Vid. Selsk. Math.-Phys. Medd. 15 (1937), 77 pp.
  • ––––, Surface transformation classes of algebraically finite type, Danske Vid. Selsk. Math.-Phys. Medd. 21 (1944), 89 pp.
  • W.P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988), 417–431.