Shadow world evaluation of the Yang-Mills measure

Details Shadow world evaluation of the Yang-Mills measure Shadow world evaluation of the Yang-Mills measure

2002-05-17

arxiv.org/abs/math/0205193v2

Algebr. Geom. Topol. 4 (2004) 311-332

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-17.abs.html

Scientific paper

A new state-sum formula for the evaluation of the Yang-Mills measure in the Kauffman bracket skein algebra of a closed surface is derived. The formula extends the Kauffman bracket to diagrams that lie in surfaces other than the plane. It also extends Turaev's shadow world invariant of links in a circle bundle over a surface away from roots of unity. The limiting behavior of the Yang-Mills measure when the complex parameter approaches -1 is studied. The formula is applied to compute integrals of simple closed curves over the character variety of the surface against Goldman's symplectic measure.

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