On the holomorphic point of view in the theory of quantum knot invariants

Details On the holomorphic point of view in the theory of quantum knot invariants On the holomorphic point of view in the theory of quantum knot invariants

2008-12-04

arxiv.org/abs/0812.1039v1

Journal of Geometry and Physics, 56 (2006), 2163-2176

Mathematics

Quantum Algebra

Scientific paper

10.1016/j.geomphys.2005.11.012

In this paper we describe progress made toward the construction of the Witten-Reshetikhin-Turaev theory of knot invariants from the geometric point of view. This is done in the perspective of a joint result of the author with A. Uribe which relates the quantum group and the Weyl quantizations of the moduli space of flat SU(2)-connections on the tours. Two results are emphasized: the reconstruction from Weyl quantization of the restriction to the torus of the modular functor, and a description of a basis of the space of quantum observables on the torus in terms of colored curves, which answers a question related to quantum computing.

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