The SU(3) Casson invariant for 3-manifolds split along a 2-sphere or a 2-torus

We describe the definition of the SU(3) Casson invariant and outline an argument which determines the contribution of certain types of components of the flat moduli space. Two applications of these methods are detailed. The first is a connected sum formula for the SU(3) Casson invariant [J. Differential Geom. 53 (1999) 443–465]. The second presents a strategy for computing the SU(3) Casson invariant for certain graph manifolds.