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

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 $n \geq 3$ twists and give a partial result.

Keywords

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

Mathematical Subject Classification 2000

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

Hessam Hamidi-Tehrani
BCC of the City University of New York Bronx NY 10453 USA

Volume 2, issue 2 (2002)

Hessam Hamidi-Tehrani