Gauge theoretic invariants of Dehn surgeries on knots

H. U. Boden, C. M. Herald, P. A. Kirk, E. P. Klassen

New methods for computing a variety of gauge theoretic invariants for homology 3-spheres obtained by Dehn surgery on knots 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 are computed for 1/k surgery on (2,q) torus knots. These results are applied to compute the SU(3) gauge theoretic Casson invariant introduced by Boden and Herald for several families of surgeries on (2,q) torus knots.