Yang-Mills测度的阴影世界估计
Shadow world evaluation of the Yang-Mills measure
摘要：
导出了一个新的计算闭曲面的Kauffman括号串代数中Yang-Mills测度的状态和公式。该公式将考夫曼括号扩展到位于平面以外的曲面上的图。它还扩展了Turaev的阴影世界不变量的链接在一个表面上的圆束远离根的单位。研究了复参数趋于-1时Yang-Mills测度的极限行为。应用该公式计算了简单闭曲线在Goldman辛测度下在曲面特征簇上的积分。
英文摘要：
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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