English

Gauge Theoretic Invariants of, Dehn Surgeries on Knots

Geometric Topology 2014-12-10 v3 Differential Geometry

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.

Keywords

Cite

@article{arxiv.math/9908020,
  title  = {Gauge Theoretic Invariants of, Dehn Surgeries on Knots},
  author = {Hans U Boden and Christopher M Herald and Paul A Kirk and Eric P Klassen},
  journal= {arXiv preprint arXiv:math/9908020},
  year   = {2014}
}

Comments

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