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A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds, II

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Abstract

We extend the results of our previous paper [1] from knots to links by using a formula for the Jones polynomial of a link derived recently by N. Reshetikhin. We establish a relation between the parameters of this formula and the multivariable Alexander polynomial. This relation is illustrated by an example of a torus link. We check that our expression for the Alexander polynomial satisfies some of its basic properties. Finally we derive a link surgery formula for the loop corrections to the trivial connection contribution to Witten's invariant of rational homology spheres.

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Authors and Affiliations

  1. Physics Department, University of Miami, P.O. Box 248046, 33124, Coral Gables, FL, USA

    L. Rozansky

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  1. L. Rozansky
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Communicated by G. Felder

Work supported by the National Science Foundation under Grant No. PHY-92 09978.

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Rozansky, L. A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds, II. Commun.Math. Phys. 175, 297–318 (1996). https://doi.org/10.1007/BF02102410

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  • DOI: https://doi.org/10.1007/BF02102410

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