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2004 Shadow world evaluation of the Yang–Mills measure
Charles Frohman, Joanna Kania-Bartoszynska
Algebr. Geom. Topol. 4(1): 311-332 (2004). DOI: 10.2140/agt.2004.4.311

Abstract

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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Charles Frohman. Joanna Kania-Bartoszynska. "Shadow world evaluation of the Yang–Mills measure." Algebr. Geom. Topol. 4 (1) 311 - 332, 2004. https://doi.org/10.2140/agt.2004.4.311

Information

Received: 17 April 2003; Revised: 26 March 2004; Accepted: 28 April 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1063.57013
MathSciNet: MR2077668
Digital Object Identifier: 10.2140/agt.2004.4.311

Subjects:
Primary: 57M27
Secondary: 57R56, 81T13

Rights: Copyright © 2004 Mathematical Sciences Publishers

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Vol.4 • No. 1 • 2004
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