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A Perturbative SU(3) Casson Invariant

S. E. Cappell·R. Lee·E. Y. Miller
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Abstract

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.

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S. E. Cappell, R. Lee, E. Y. Miller. 2000-06-02. A Perturbative SU(3) Casson Invariant. https://arxiv.org/abs/math/0006018

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