On abelian quantum invariants of links in 3-manifolds |
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Authors: | Florian Deloup |
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Affiliation: | (1) Université Paul Sabatier, Toulouse III, Laboratoire émile Picard de Mathématiques, 118, route de Narbonne, 31062 Toulouse, France (e-mail: deloup@picard.ups-tlse.fr) , FR |
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Abstract: | From a finite abelian group G, a quadratic form onG and an element in , we define a topological invariant of a pair(M,L) where is a closed oriented 3-manifold and L an oriented, framedn-component link inM. The main result consists in an explicit formula for this invariant, based on a reciprocity formula for Gauss sums, which features a special linking pairing. This pairing depends on both the quadratic form q and the linking pairing of M. A necessary and sufficient condition for the invariant to vanish is described in terms of a characteristic class for this pairing. We also discuss torsion spin-structures and related structures which appear in this context. Received May 13, 1998 / Accepted November 11, 1999 / Published online February 5, 2001 |
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Keywords: | Mathematics Subject Classification (2000): 11E 57N |
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