Gauge Theoretic Invariants of, Dehn Surgeries on Knots

Details Gauge Theoretic Invariants of, Dehn Surgeries on Knots Gauge Theoretic Invariants of, Dehn Surgeries on Knots

1999-08-05

arxiv.org/abs/math/9908020v3

Geom.Topol. 5 (2001) 143-226

Mathematics

Geometric Topology

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

Scientific paper

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.

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