  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.
