A lantern lemma

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.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-46.abs.html

References in corpus (1)

• Groups generated by positive multi-twists and the fake lantern problem

Cited by in corpus (4)

• On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number
• Groups generated by positive multi-twists and the fake lantern problem
• Homomorphisms between mapping class groups
• Genus two Lefschetz fibrations with $b_2^{+}=1$ and ${c_1}^2=1,2$