A lantern lemma

Dan Margalit

doi:10.2140/agt.2002.2.1179

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Home > Journals > Algebr. Geom. Topol. > Volume 2 > Issue 2 > Article

2002 A lantern lemma

Dan Margalit

Algebr. Geom. Topol. 2(2): 1179-1195 (2002). DOI: 10.2140/agt.2002.2.1179

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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.