Geometry & Topology

Gauge theoretic invariants of Dehn surgeries on knots

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

Full-text: Open access

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 1k Dehn surgery on (2,q) torus knots. The methods are then applied to compute the SU(3) gauge theoretic Casson invariant (introduced in [J. Diff. Geom. 50 (1998) 147-206]) for Dehn surgeries on (2,q) torus knots for q=3,5,7 and 9.

Article information

Source
Geom. Topol., Volume 5, Number 1 (2001), 143-226.

Dates
Received: 20 September 1999
Accepted: 7 March 2001
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513882987

Digital Object Identifier
doi:10.2140/gt.2001.5.143

Mathematical Reviews number (MathSciNet)
MR1825661

Zentralblatt MATH identifier
1065.57009

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 53D12: Lagrangian submanifolds; Maslov index 58J28: Eta-invariants, Chern-Simons invariants 58J30: Spectral flows

Keywords
homology 3–sphere gauge theory 3–manifold invariants spectral flow Maslov index

Citation

Boden, Hans U; Herald, Christopher M; Kirk, Paul A; Klassen, Eric P. Gauge theoretic invariants of Dehn surgeries on knots. Geom. Topol. 5 (2001), no. 1, 143--226. doi:10.2140/gt.2001.5.143. https://projecteuclid.org/euclid.gt/1513882987


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