Gauge theoretic invariants of Dehn surgeries on knots

Boden, Hans U¹ ; Herald, Christopher M² ; Kirk, Paul A³ ; Klassen, Eric P⁴

¹ McMaster University, Hamilton, Ontario, L8S 4K1, Canada
² University of Nevada, Reno, Nevada 89557, USA
³ Indiana University, Bloomington, Indiana 47405, USA
⁴ Florida State University, Tallahassee, Florida 32306, USA

Geometry & topology, Tome 5 (2001) no. 1, pp. 143-226.

Résumé

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.

Détail

DOI : 10.2140/gt.2001.5.143

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

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