# A perturbative SU(3) Casson invariant

### Sylvain Cappell

New York University, USA### R. Lee

New York University, USA### E. Y. Miller

New York University, USA

## Abstract

A perturbative SU(3) Casson invariant $\Lambda_{SU(3)}(X)$ for integral homology 3-sphere is defined. Besides being fully perturbative, it has the nice properties: (1) $4\cdot \Lambda_{SU(3)}$ 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. 491–523

DOI 10.1007/S00014-002-8349-8