Geometry & Topology, Vol. 5 (2001) Paper no. 6, pages 143--226.

Gauge Theoretic Invariants of Dehn Surgeries on Knots

Hans U Boden, Christopher M Herald, Paul A Kirk, Eric P Klassen

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. Homology 3--sphere, gauge theory, 3--manifold invariants, spectral flow, Maslov index

AMS subject classification. Primary: 57M27. Secondary: 53D12, 58J28, 58J30.

DOI: 10.2140/gt.2001.5.143

E-print: arXiv:math.GT/9908020

Submitted to GT on 20 September 1999. Paper accepted 7 March 2001. Paper published 21 March 2001.

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Hans U Boden, Christopher M Herald, Paul A Kirk, Eric P Klassen
McMaster University, Hamilton, Ontario L8S 4K1, Canada
University of Nevada, Reno, Nevada 89557, USA
Indiana University, Bloomington, Indiana 47405, USA
Florida State University, Tallahassee, Florida 32306, USA
Email: boden@math.mcmaster.ca, herald@unr.edu, pkirk@indiana.edu, klassen@zeno.math.fsu.edu

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