Kauffman bracket skein module of the connected sum of handlebodies: a counterexample

被引：0
作者：
Rhea Palak Bakshi
Józef H. Przytycki
机构：
[1] The George Washington University,Department of Mathematics
[2] University of Gdańsk,Department of Mathematics
来源：
manuscripta mathematica | 2022年 / 167卷
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Primary: 57K31; Secondary: 57K10;
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摘要：
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.
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页码：809 / 820
页数：11
相关论文
共 9 条
[1]  
Hoste J(1993)The J. Knot Theory Ramif. 2 321-333
[2]  
Przytycki JH(1995)-skein module of lens spaces; a generalization of the Jones polynomial Math. Z. 220 65-73
[3]  
Hoste J(1987)The Kauffman bracket skein module of Topology 26 395-407
[4]  
Przytycki JH(2011)State models and the Jones polynomial J. Knot Theory Ramif. 20 651-675
[5]  
Kauffman LH(1991)Kauffman bracket skein module of the connected sum of two projective spaces Bull. Pol. Acad. Sci. Math. 39 91-100
[6]  
Mroczkowski M(1999)Skein modules of 3-manifolds Kobe Math. J. 16 45-66
[7]  
Przytycki JH(2000)Fundamentals of Kauffman bracket skein modules Manuscr. Math. 101 199-207
[8]  
Przytycki JH(undefined)Kauffman bracket skein module of a connected sum of undefined undefined undefined-undefined
[9]  
Przytycki JH(undefined)-manifolds undefined undefined undefined-undefined
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