  We calculate the self-Floer cohomology with Z/2 coefficients of some immersed
Lagrangian spheres in the affine symplectic submanifolds of C^3 that are
smoothings of A_N surfaces. The immersed spheres are exact and graded.
Moreover, they satisfy a positivity assumption that allows us to calculate the
Floer cohomology as follows: Given auxiliary data a Morse function on S^2 and a
time-dependent almost complex structure, the Floer cochain complex is the Morse
complex plus two generators for each self-intersection point of the Lagrangian
sphere. The Floer differential is defined by counting combinations of Morse
flow lines and holomorphic strips. Using a Lefschetz fibration allows us to
explicitly calculate all holomorphic strips and describe the Floer
differential. For most of the immersed spheres the Floer differential is zero
(with Z/2-coefficients).
