Geometry & Topology

Dehn twists have roots

Dan Margalit and Saul Schleimer

Full-text: Open access

Abstract

We show that every Dehn twist in the mapping class group of a closed, connected, orientable surface of genus at least two has a nontrivial root.

Article information

Source
Geom. Topol., Volume 13, Number 3 (2009), 1495-1497.

Dates
Received: 31 October 2008
Revised: 30 December 2008
Accepted: 31 December 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800252

Digital Object Identifier
doi:10.2140/gt.2009.13.1495

Mathematical Reviews number (MathSciNet)
MR2496051

Zentralblatt MATH identifier
1203.57007

Subjects
Primary: 20F28: Automorphism groups of groups [See also 20E36]

Keywords
Dehn twist root mapping class group Nielsen transformation elementary matrix

Citation

Margalit, Dan; Schleimer, Saul. Dehn twists have roots. Geom. Topol. 13 (2009), no. 3, 1495--1497. doi:10.2140/gt.2009.13.1495. https://projecteuclid.org/euclid.gt/1513800252


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References

  • J S Birman, H M Hilden, On the mapping class groups of closed surfaces as covering spaces, from: “Advances in the theory of Riemann surfaces (Proc. Conf., Stony Brook, N.Y., 1969)”, (L V Ahlfors et al, editors), Ann. of Math. Studies 66, Princeton Univ. Press (1971) 81–115
  • C Labruère, L Paris, Presentations for the punctured mapping class groups in terms of Artin groups, Algebr. Geom. Topol. 1 (2001) 73–114