A large \(k\) asymptotics of Witten’s invariant of Seifert manifolds. (English) Zbl 0837.57014
Summary: We calculate a large \(k\) asymptotic expansion of the exact surgery formula for Witten’s SU(2) invariant of some 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.
MSC:
| 57N10 | Topology of general \(3\)-manifolds (MSC2010) |
| 81T99 | Quantum field theory; related classical field theories |
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