Dehn twists and free subgroups of symplectic mapping class groups (Q2928218)

The aim of the paper is to find conditions under which the Dehn twists about two Lagrangian spheres in an exact symplectic manifold generate a free non-abelian subgroup of the symplectic mapping class group. Such a condition is given by the main theorem which says that if \(M\) is an exact symplectic manifold with contact type boundary and \(L\) and \(L'\) are two Lagrangian spheres such that the dimension of the Floer cohomology group \(HF(L,L')\) is at least 2, then the Dehn twists \(\tau_{L}\) and \(\tau_{L'}\) generate a free subgroup of symplectomorphisms of \(M\). Examples of such spheres in the Milnor fibers of all degenerate isolated hypersurface singularities are provided.