A Perturbative SU(3) Casson Invariant
Abstract
A perturbative SU(3) Casson invariant SU(3)(X) for integral homology 3-spheres is defined. Besides being fully perturbative, it has nice properties: (1) 4 . 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.