Algebraic and Geometric Topology 2 (2002), paper no. 46, pages 1179-1195.

A lantern lemma

Dan Margalit

Abstract. We show that in the mapping class group of a surface any relation between Dehn twists of the form T_x^j T_y^k = M (M a multitwist) is the lantern relation, and any relation of the form (T_x T_y)^k = M (where T_x commutes with M) is the 2-chain relation.

Keywords. Mapping class group, Dehn twist, lantern relation

AMS subject classification. Primary: 57M07. Secondary: 20F38, 57N05.

DOI: 10.2140/agt.2002.2.1179

E-print: arXiv:math.GT/0206120

Submitted: 21 June 2002. Accepted: 17 December 2002. Published: 27 December 2002.

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Dan Margalit
Department of Mathematics, 5734 S University Ave
Chicago, IL 60637-1514, USA
Email: margalit@math.uchicago.edu
URL: http://www.math.uchicago.edu/margalit
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