A lantern lemma

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

Mathematical Subject Classification 2000

Primary: 57M07

Secondary: 20F38, 57N05

References

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Publication

Received: 21 June 2002

Accepted: 17 December 2002

Published: 27 December 2002

Authors

Dan Margalit
Department of Mathematics 5734 S University Ave Chicago, IL 60637-1514 USA

Volume 2, issue 2 (2002)

Dan Margalit