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

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

2002-06-12

arxiv.org/abs/math/0206131v2

Algebr. Geom. Topol. 2 (2002) 1155-1178

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-45.abs.html

Scientific paper

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.

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