  We study the symplectic topology of some finite algebraic quotients of the An
Milnor fibre which are diffeomorphic to the rational homology balls that appear
in Fintushel and Stern's rational blowdown construction. We prove that these
affine surfaces have no closed exact Lagrangian submanifolds by using the
already available and deep understanding of the Fukaya category of the An
Milnor fibre coming from homological mirror symmetry. On the other hand, we
find Floer theoretically essential monotone Lagrangian tori, finitely covered
by the monotone tori which we study in the An Milnor fibre. We conclude that
these affine surfaces have non-vanishing symplectic cohomology.
