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A largek asymptotics of Witten's invariant of Seifert manifolds

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Abstract

We calculate a largek asymptotic expansion of the exact surgery formula for Witten'sSU(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.

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Authors and Affiliations

  1. Theory Group, Department of Physics, University of Texas at Austin, 78712-1081, Austin, TX, U.S.A.

    L. Rozansky

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  1. L. Rozansky
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Communicated by N.Yu. Reshetikhin

Work supported by NSF Grant 9009850 and R.A. Welch Foundation.

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Rozansky, L. A largek asymptotics of Witten's invariant of Seifert manifolds. Commun.Math. Phys. 171, 279–322 (1995). https://doi.org/10.1007/BF02099272

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  • DOI: https://doi.org/10.1007/BF02099272

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