A Large k Asymptotics of Witten's Invariant of Seifert Manifolds

Abstract

We calculate a large $k$ asymptotic expansion of the exact surgery formula for Witten's $SU(2)$ invariant of Seifert manifolds. The contributions of all flat connections are identified. An agreement with the 1-loop formula is checked. A contribution of the irreducible connections appears to contain only a finite number of terms in the asymptotic series. A 2-loop correction to the contribution of the trivial connection is found to be proportional to Casson's invariant.

51 pages (Some changes are made to the Discussion section. A surgery formula for perturbative corrections to the contribution of the trivial connection is suggested.)

References in corpus (2)

• Two Dimensional Gauge Theories Revisited
• S and T matrices for the super $U(1,1)$ WZW model. Application to surgery and 3-manifold invariants based on the Alexander Conway polynomial

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