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

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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 languageEnglish
Pages (from-to)2163-2176
Number of pages14
JournalJournal of Geometry and Physics
Volume56
Issue number10
DOIs
StatePublished - Oct 2006

Keywords

  • Modular functor
  • Theta functions
  • Weyl quantization
  • Witten-Reshetikhin-Turaev invariants

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