The SU(3) Casson Invariant for Integral Homology 3-Spheres
Hans U. Boden, Christopher M. Herald
TL;DR
This paper introduces a new gauge theoretic invariant for integral homology 3-spheres based on counting perturbed flat SU(3) connections, extending Casson’s invariant from SU(2) to SU(3).
Contribution
It generalizes Walker's correction term, providing a comprehensive formula for the SU(3) Casson invariant that accounts for reducible and irreducible connections.
Findings
Defines a gauge invariant counting irreducible flat SU(3) connections.
Includes a correction term for reducible connections extending Walker's work.
Provides a formula applicable to integral homology 3-spheres.
Abstract
We derive a gauge theoretic invariant of integral homology 3-spheres which counts gauge orbits of irreducible, perturbed flat SU(3) connections with sign given by spectral flow. To compensate for the dependence of this sum on perturbations, the invariant includes contributions from the reducible, perturbed flat orbits. Our formula for the correction term generalizes that given by Walker in his extension of Casson's SU(2) invariant to rational homology 3-spheres.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics