Dehn twists and free subgroups of symplectic mapping class groups

Details Dehn twists and free subgroups of symplectic mapping class groups Dehn twists and free subgroups of symplectic mapping class groups

2012-04-12

arxiv.org/abs/1204.2851v1

Mathematics

Symplectic Geometry

34 pages, 7 figures

Scientific paper

Given two Lagrangian spheres in an exact symplectic manifold, we find conditions under which the Dehn twists about them generate a free non-abelian subgroup of the symplectic mapping class group. This extends a result of Ishida for Riemann surfaces. The proof generalises the categorical version of Seidel's long exact sequence to arbitrary powers of a fixed Dehn twist. We also show that the Milnor fibre of any isolated degenerate hypersurface singularity contains such pairs of spheres.

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