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.
Notes on file formats
Hessam Hamidi-Tehrani
B.C.C. of the City University of New York
Bronx, NY 10453, USA
Email: hessam@math.columbia.edu
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