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Kauffman bracket skein module of the connected sum of handlebodies: a counterexample
manuscripta mathematica ( IF 0.5 ) Pub Date : 2021-03-15 , DOI: 10.1007/s00229-021-01288-5
Rhea Palak Bakshi , Józef H. Przytycki

In this paper we provide a counterexample to a 22-year-old theorem about the structure of the Kauffman bracket skein module of the connected sum of two handlebodies. We achieve this by analysing handle slidings on compressing discs in a handlebody. We find more relations than previously predicted for the Kauffman bracket skein module of the connected sum of handlebodies, when one of them is not a solid torus. Additionally, we speculate on the structure of the Kauffman bracket skein module of the connected sum of two solid tori.



中文翻译:

连接的车体总和的Kauffman支架绞线模块:一个反例

在本文中,我们提供了一个22岁的定理的反例,该定理关于两个车体的连接总和的Kauffman支架绞链模块的结构。我们通过分析手柄主体中压缩盘上的手柄滑动来实现这一点。当其中一个不是坚固的圆环时,我们发现的关系比以前对连接的和体的Kauffman支架绞线模块的预测要多。另外,我们推测了两个实心花托的连接总和的Kauffman支架绞线模块的结构。

更新日期:2021-03-15
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