Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 078, 30 pages      arXiv:0801.1445      http://dx.doi.org/10.3842/SIGMA.2008.078

Deligne-Beilinson Cohomology and Abelian Link Invariants

Enore Guadagnini a and Frank Thuillier b
a) Dipartimento di Fisica ''E. Fermi'' dell'Università di Pisa and Sezione di Pisa dell'INFN, Italy
b) LAPTH, Chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux cedex, France

Received July 14, 2008, in final form October 27, 2008; Published online November 11, 2008

Abstract
For the Abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and we derive the main properties of the observables in a generic closed orientable 3-manifold. We present an explicit path-integral non-perturbative computation of the Chern-Simons link invariants in the case of the torsion-free 3-manifolds S3, S1 × S2 and S1 × Σg.

Key words: Deligne-Beilinson cohomology; Abelian Chern-Simons; Abelian link invariants.

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