A Perturbative SU(3) Casson Invariant
S. E. Cappell, R. Lee, E. Y. Miller
Abstract
A perturbative SU(3) Casson invariant ΛSU(3)(X) for integral homology 3-spheres is defined. Besides being fully perturbative, it has nice properties: (1) 4 . ΛSU(3)(X) is an integer. (2) It is preseved under orientation change. (3) A connected sum formula holds. Explicit calculations of the invariant for 1/k surgery on (2,q) torus knots are made and compared with a different generalization of Casson's invariant to SU(3) by Boden and Herald. For those cases computed, the invariant defined here is a quadratic polynomial in k for k>0 and a quadratic polynomial for k<0.
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