#### Volume 5, issue 1 (2001)

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Gauge theoretic invariants of Dehn surgeries on knots

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

Geometry & Topology 5 (2001) 143–226
 arXiv: math.GT/9908020
##### 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 $SU\left(2\right)$ representations. These quantities are calculated for flat $SU\left(2\right)$ connections on homology 3–spheres obtained by $1∕k$ Dehn surgery on $\left(2,q\right)$ torus knots. The methods are then applied to compute the $SU\left(3\right)$ gauge theoretic Casson invariant (introduced in [J. Diff. Geom. 50 (1998) 147-206]) for Dehn surgeries on $\left(2,q\right)$ torus knots for $q=3,5,7$ and 9.

##### Keywords
homology 3–sphere, gauge theory, 3–manifold invariants, spectral flow, Maslov index
##### Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 53D12, 58J28, 58J30