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Dehn twists have roots

Dan Margalit and Saul Schleimer
Geometry & Topology 13 (2009) 1495–1497
DOI: 10.2140/gt.2009.13.1495
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.

Keywords
Dehn twist, root, mapping class group, Nielsen transformation, elementary matrix
Mathematical Subject Classification 2000
Primary: 20F28
References
Publication
Received: 31 October 2008
Revised: 30 December 2008
Accepted: 31 December 2008
Published: 3 March 2009
Proposed: Walter Neumann
Seconded: Joan Birman, Rob Kirby
Authors
Dan Margalit
Department of Mathematics
503 Boston Ave
Tufts University
Medford, MA 02155
USA
Saul Schleimer
Department of Mathematics
University of Warwick
Coventry, CV4 7AL
UK