  Suppose Y is an integer homology 3-sphere, Taubes proved that the number of
irreducible critical orbits of the perturbed Chern-Simons functional on Y,
counted with signs, is equal to the algebraic intersection number of two
character varieties associated with Heegaard splittings when the structure
group is SU(2). Taubes' result established a relationship between gauge theory
and the Casson invariant. This article proves an analogous identification
result for SU(n) generalized Casson invariants. As a special case, we show that
the SU(3) Casson invariant of Boden-Herald can be equivalently calculated by
taking an appropriate intersection number of Lagrangian submanifolds.
