Gauge theoretic invariants of Dehn surgeries on knots

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 $S U (2)$ representations. These quantities are calculated for flat $S U (2)$ connections on homology 3–spheres obtained by $1 ∕ k$ Dehn surgery on $(2, q)$ torus knots. The methods are then applied to compute the $S U (3)$ 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

References

Forward citations

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

Volume 5, issue 1 (2001)

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