Rocky Mountain Journal of Mathematics

On roots of Dehn twists

Naoyuki Monden

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Abstract

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

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

Dates
First available in Project Euclid: 28 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1411945675

Digital Object Identifier
doi:10.1216/RMJ-2014-44-3-987

Mathematical Reviews number (MathSciNet)
MR3264493

Zentralblatt MATH identifier
1302.57056

Citation

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. https://projecteuclid.org/euclid.rmjm/1411945675


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References

  • 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.