Geodesic
Groups generated by positive multi-twists and the fake lantern problem
Hamidi-Tehrani, Hessam1
1BCC of the City University of New York, Bronx NY 10453, USA
Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 1155-1178
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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.

DOI : 10.2140/agt.2002.2.1155
Keywords: mapping class group, Dehn twist, multi-twist, pseudo-Anosov, lantern relation

Hamidi-Tehrani, Hessam  1

1 BCC of the City University of New York, Bronx NY 10453, USA 
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Hamidi-Tehrani, Hessam. Groups generated by positive multi-twists and the fake lantern problem. Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 1155-1178. doi: 10.2140/agt.2002.2.1155

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