A Perturbative SU(3) Casson Invariant

Details A Perturbative SU(3) Casson Invariant A Perturbative SU(3) Casson Invariant

2000-06-02

arxiv.org/abs/math/0006018v1

Mathematics

Differential Geometry

39 pages, 4 tables

Scientific paper

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