Algebraic & Geometric Topology 2 (2002) 1155–1178

DOI: 10.2140/agt.2002.2.1155

arXiv: math.GT/0206131

Abstract

Let Γ be a group generated by two positive multi-twists. We give some sufficient conditions for Γ to be free or have no “unexpectedly reducible” elements. For a group Γ generated by two Dehn twists, we classify the elements in Γ which are multi-twists. As a consequence we are able to list all the lantern-like relations in the mapping class groups. We classify groups generated by powers of two Dehn twists which are free, or have no “unexpectedly reducible” elements. In the end we pose similar problems for groups generated by powers of n ≥ 3 twists and give a partial result.

Keywords

mapping class group, Dehn twist, multi-twist, pseudo-Anosov, lantern relation

Mathematical Subject Classification

Primary: 57M07

Secondary: 20F38, 57N05

References

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Publication

Received: 12 June 2002
Revised: 8 November 2002
Accepted: 17 December 2002
Published: 27 December 2002

Authors