Algebraic and Geometric Topology 2 (2002), paper no. 45, pages 1155-1178.

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

Hessam Hamidi-Tehrani

Abstract. Let Gamma be a group generated by two positive multi-twists. We give some sufficient conditions for Gamma to be free or have no `unexpectedly reducible' elements. For a group Gamma generated by two Dehn twists, we classify the elements in Gamma 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 > 2 twists and give a partial result.

Keywords. Mapping class group, Dehn twist, multi-twist, pseudo-Anosov, lantern relation

AMS subject classification. Primary: 57M07. Secondary: 20F38, 57N05.

DOI: 10.2140/agt.2002.2.1155

E-print: arXiv:math.GT/0206131

Submitted: 12 June 2002. (Revised: 8 November 2002.) Accepted: 17 December 2002. Published: 27 December 2002.

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Hessam Hamidi-Tehrani
B.C.C. of the City University of New York
Bronx, NY 10453, USA

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