JournalscmhVol. 77 , No. 3DOI 10.1007/s00014-002-8349-8

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

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.