A perturbative SU(3) Casson invariant for integral homology 3-sphere is defined. Besides being fully perturbative, it has the nice properties: (1) is an integer. (2) It is preserved under orientation change. (3) A connect sum formula. Explicit calculations of the invariant for 1/k surgery of (2, q) torus knot are presented and compared with Boden-Herald‘s different SU(3) generalization of Casson‘s invariant. For those cases computed, the invariant defined here is a quadratic polynomial in k for k > 0 and a different quadratic polynomial for k < 0.
Cite this article
Sylvain Cappell, R. Lee, E. Y. Miller, A perturbative SU(3) Casson invariant. Comment. Math. Helv. 77 (2002), no. 3, pp. 491–523DOI 10.1007/S00014-002-8349-8