JournalscmhVol. 77, No. 3pp. 491–523

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
A perturbative SU(3) Casson invariant cover
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Abstract

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