  A $g$-tuple of disjoint, linearly independent circles in a Riemann surface of
genus $g$ determines a `Heegaard torus' in its $g$-fold symmetric product.
Changing the circles by a handleslide produces a new torus. It is proved that,
for symplectic forms with certain properties, these two tori are
Hamiltonian-isotopic Lagrangian submanifolds. This provides an alternative
route to the handleslide-invariance of Ozsvath-Szabo's Heegaard Floer homology.
