Geometry & Topology

Gauge theoretic invariants of Dehn surgeries on knots

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 [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

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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