A Perturbative SU(3) Casson Invariant

Cappell, S. E.; Lee, R.; Miller, E. Y.

A Perturbative SU(3) Casson Invariant

Authors

Cappell, S. E.

Lee, R.

Miller, E. Y.

Description

A perturbative SU(3) Casson invariant $Λ_{SU(3)}(X)$ for integral homology 3-spheres is defined. Besides being fully perturbative, it has nice properties: (1) $4 . Λ_{SU(3)}(X)$ 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.
39 pages, 4 tables