English

The Kauffman skein algebra of a surface at $\sqrt{-1}$

Geometric Topology 2008-02-07 v1 Quantum Algebra

Abstract

We study the structure of the Kauffman algebra of a surface with parameter equal to sqrt(-1). We obtain an interpretation of this algebra as an algebra of parallel transport operators acting on sections of a line bundle over the moduli space of flat connections in a trivial SU(2)-bundle over the surface. We analyse the asymptotics of traces of curve-operators in TQFT in non standard regimes where the root of unity parametrizing the TQFT accumulates to a root of unity. We interpret the case of sqrt(-1) in terms of parallel transport operators.

Keywords

Cite

@article{arxiv.0802.0812,
  title  = {The Kauffman skein algebra of a surface at $\sqrt{-1}$},
  author = {Julien Marche},
  journal= {arXiv preprint arXiv:0802.0812},
  year   = {2008}
}

Comments

16 pages, 2 figures