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

Hessam Hamidi-Tehrani

Algebraic & Geometric Topology 2 (2002) 1155–1178

arXiv: math.GT/0206131


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.

mapping class group, Dehn twist, multi-twist, pseudo-Anosov, lantern relation
Mathematical Subject Classification 2000
Primary: 57M07
Secondary: 20F38, 57N05
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Received: 12 June 2002
Revised: 8 November 2002
Accepted: 17 December 2002
Published: 27 December 2002
Hessam Hamidi-Tehrani
BCC of the City University of New York
Bronx NY 10453