2000/06/02 by Sylvain E. Cappell, S. E. Cappell, Cappell, S. E. +4
Mathematics · #57M05 #57M25 #58G25 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:57M05 #msc:57M25 #msc:58G25
paper · pdf · doi:10.48550/arxiv.math/0006018
39 pages, 4 tables
arxiv created 2000/06/02 · openalex publication_date 2000/06/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A perturbative SU(3) Casson invariant ΛSU(3)(X) for integral homology 3-spheres is defined. Besides being fully perturbative, it has nice properties: (1) 4 . ΛSU(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.