The integer valued SU(3) Casson invariant for Brieskorn spheres

We develop techniques for computing the integer valued SU(3) Casson invariant defined in [6]. Our method involves resolving the singularities in the flat moduli space using a twisting perturbation and analyzing its effect on the topology of the perturbed flat moduli space. These techniques, together with Bott-Morse theory and the splitting principle for spectral flow, are applied to calculate τSU(3)(Σ) for all Brieskorn homology spheres.