#### Volume 2, issue 2 (2002)

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A lantern lemma

### Dan Margalit

Algebraic & Geometric Topology 2 (2002) 1179–1195
 arXiv: math.GT/0206120
##### 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 ${\left({T}_{x}{T}_{y}\right)}^{k}=M$ (where ${T}_{x}$ commutes with $M$) is the 2–chain relation.

##### Keywords
mapping class group, Dehn twist, lantern relation
##### Mathematical Subject Classification 2000
Primary: 57M07
Secondary: 20F38, 57N05