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arXiv · 1204.2851

Dehn twists and free subgroups of symplectic mapping class groups

Ailsa Keating
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Abstract

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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Ailsa Keating. 2013-06-17. Dehn twists and free subgroups of symplectic mapping class groups. https://doi.org/10.1112/jtopol%2Fjtt033

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