Quasi-quantum groups,knots, three-manifolds,and topological field theory |
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Authors: | Daniel Altschuler Antoine Coste |
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Institution: | (1) Theory Division, CERN, CH-1211 Genève 23, Switzerland;(2) Chemin de Bellevue, LAPP, BP 110, F-74941 Annecy-le-Vieux Cedex, France;(3) Present address: Centre de Physique Théorique, CNRS Marseille-Luminy, Marseille-Luminy, France |
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Abstract: | We show how to construct, starting from a quasi-Hopf algebra, or quasiquantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite groupG, and a 3-cocycle , which was first studied by Dijkgraaf, Pasquier, and Roche. We treat this example in more detail, and argue that in this case the invariants agree with the partition function of the topological field theory of Dijkgraaf and Witten depending on the same dataG, . |
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