Abstract
In this paper we describe progress made toward the construction of the Witten-Reshetikhin-Turaev theory of knot invariants from a 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 torus. 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.
Original language | English |
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Pages (from-to) | 2163-2176 |
Number of pages | 14 |
Journal | Journal of Geometry and Physics |
Volume | 56 |
Issue number | 10 |
DOIs | |
State | Published - Oct 2006 |
Keywords
- Modular functor
- Theta functions
- Weyl quantization
- Witten-Reshetikhin-Turaev invariants