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

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

2008-02-06

arxiv.org/abs/0802.0812v1

Mathematics

Geometric Topology

16 pages, 2 figures

Scientific paper

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.

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