We develop techniques for computing the integer valued SU(3) Casson invariant defined in . 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.
"The integer valued SU(3) Casson invariant for Brieskorn spheres." J. Differential Geom. 71 (1) 23 - 83, September 2005. https://doi.org/10.4310/jdg/1143644312