Volume 5, issue 1 (2001)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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(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.

Keywords
homology 3–sphere, gauge theory, 3–manifold invariants, spectral flow, Maslov index
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 53D12, 58J28, 58J30
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Publication
Received: 20 September 1999
Accepted: 7 March 2001
Published: 21 March 2001
Proposed: Tomasz Mrowka
Seconded: Ronald Fintushel, Ronald Stern
Authors
Hans U Boden
McMaster University
Hamilton
Ontario
L8S 4K1
Canada
Christopher M Herald
University of Nevada
Reno
Nevada 89557
USA
Paul A Kirk
Indiana University
Bloomington
Indiana 47405
USA
Eric P Klassen
Florida State University
Tallahassee
Florida 32306
USA