Kauffman brackets, character varieties, and triangulations of surfaces
Kauffman brackets, character varieties, and triangulations of surfaces
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考夫曼括号、字符变化和曲面三角剖分
DOI：
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发表时间：
2010
期刊：
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通讯作者：
H. Wong
中科院分区：
文献类型：
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作者：
F. Bonahon;H. Wong
曲面上的Kauffman括号是加厚曲面上框架链的不变量，满足Kauffman skein关系，在叠加下是乘法的。这包括曲面的绞链代数的表示。我们展示了如何一个不可约表示的绞代数通常指定一个点的特征多样性的同态从基本群的表面PSL_2（C），以及某些权重相关的穿刺的表面。相反，我们勾勒出一个事实，即每个点的字符品种，赋予适当的穿刺重量，唯一地确定了考夫曼括号的证明。细节将出现在其他地方。
A Kauffman bracket on a surface is an invariant for framed links in the thickened surface, satisfying the Kauffman skein relation and multiplicative under superposition. This includes representations of the skein algebra of the surface. We show how an irreducible representation of the skein algebra usually specifies a point of the character variety of homomorphisms from the fundamental group of the surface to PSL_2(C), as well as certain weights associated to the punctures of the surface. Conversely, we sketch a proof of the fact that each point of the character variety, endowed with appropriate puncture weights, uniquely determines a Kauffman bracket. Details will appear elsewhere.