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AN ANALYTIC APPROACH TO TURAEV'S SHADOW INVARIANT

ATLE HAHN

Grupo de Físca Matemática da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa, Portugal

https://doi.org/10.1142/S021821650800666XCited by:4 (Source: Crossref)

Abstract

In the present paper, we extend the "torus gauge fixing" approach by Blau and Thompson, which was developed in [10] for the study of Chern–Simons models with base manifolds M of the form M = Σ × S¹, in a suitable way. We arrive at a heuristic path integral formula for the Wilson loop observables associated to general links in M. We then show that the right-hand side of this formula can be evaluated explicitly in a non-perturbative way and that this evaluation naturally leads to the face models in terms of which Turaev's shadow invariant is defined.

Keywords:

AMSC: 57M27, 60H40, 81T08, 81T45

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