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29 March 2024
 
  » arxiv » math.GT/9908020

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Gauge Theoretic Invariants of, Dehn Surgeries on Knots
Hans U Boden ; Christopher M Herald ; Paul A Kirk ; Eric P Klassen ;
Date 5 Aug 1999
Journal Geom.Topol. 5 (2001) 143-226
Subject Geometric Topology; Differential Geometry MSC-class: 57M27, 53D12, 58J28, 58J30 | math.GT math.DG
AbstractNew 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.
Source arXiv, math.GT/9908020
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