Shadow world evaluation of the Yang–Mills measure

Frohman, Charles¹ ; Kania-Bartoszynska, Joanna²

¹Department of Mathematics, University of Iowa, Iowa City IA 52242, USA
²Department of Mathematics, Boise State University, Boise ID 83725, USA

Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 311-332

Résumé

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.

Détail

DOI : 10.2140/agt.2004.4.311

Keywords: Yang–Mills measure, shadows, links, skeins, $SU(2)$–characters of a surface

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