光纤链路的非半简单sl2量子不变量

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-08-19 DOI:10.1016/j.aim.2025.110494

Daniel López Neumann, Roland van der Veen

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引用次数: 0

摘要

Akutsu-Deguchi-Ohtsuki （ADO）不变量是研究最多的来自非半简单张量范畴的量子链接不变量。我们证明，对于S3中的纤维链路，ADO不变量的程度由属决定，顶部系数是统一的根。更准确地说，我们证明了顶部系数是由与纤维表面相关的S3平面场的Hopf不变量决定的。我们的证明是基于我们以前的工作中建立的属界，以及吉鲁-古德曼定理，该定理表明三球中的纤维表面可以通过管道/管道Hopf带从圆盘中获得。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Non-semisimple sl2 quantum invariants of fibred links

The Akutsu-Deguchi-Ohtsuki (ADO) invariants are the most studied quantum link invariants coming from a non-semisimple tensor category. We show that, for fibred links in

S^{3}

, the degree of the ADO invariant is determined by the genus and the top coefficient is a root of unity. More precisely, we prove that the top coefficient is determined by the Hopf invariant of the plane field of

S^{3}

associated to the fiber surface. Our proof is based on the genus bounds established in our previous work, together with a theorem of Giroux-Goodman stating that fiber surfaces in the three-sphere can be obtained from a disk by plumbing/deplumbing Hopf bands.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.