Gauge Theoretic Invariants of, Dehn Surgeries on Knots

Abstract

New methods for computing a variety of gauge theoretic invariants for homology 3-spheres are developed. These invariants include the Chern-Simons invariants, the spectral flow of the odd signature operator, and the rho invariants of irreducible SU(2) representations. These quantities are calculated for flat SU(2) connections on homology 3-spheres obtained by 1/k Dehn surgery on (2,q) torus knots. The methods are then applied to compute the SU(3) gauge theoretic Casson invariant (introduced in [H U Boden and C M Herald, The SU(3) Casson invariant for integral homology 3--spheres, J. Diff. Geom. 50 (1998) 147-206]) for Dehn surgeries on (2,q) torus knots for q=3,5,7 and 9.

Version 3: minor corrections from version 2. Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper6.abs.html

References in corpus (2)

• The SU(3) Casson Invariant for Integral Homology 3-Spheres
• Fermat limit and congruence of Ohtsuki invariants

Cited by in corpus (8)

• SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
• Surface Operators and Knot Homologies
• The pillowcase and perturbations of traceless representations of knot groups
• A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds
• A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of SU(2) connections
• Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles
• Splitting the spectral flow and the SU(3) Casson invariant for spliced sums
• On the rho invariant for manifolds with boundary