تقرير
Non-semisimple $\mathfrak{sl}_2$ quantum invariants of fibred links
| العنوان: | Non-semisimple $\mathfrak{sl}_2$ quantum invariants of fibred links |
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| المؤلفون: | Neumann, Daniel López, van der Veen, Roland |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Quantum Algebra, Mathematics - Geometric Topology, 57K16, 57K10, 20G42 |
| الوصف: | The Akutsu-Deguchi-Ohtsuki (ADO) invariants are the most studied quantum link invariants coming from a non-semisimple tensor category. We show that, for fibered 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. Comment: 18 pages, comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.15561 |
| رقم الأكسشن: | edsarx.2407.15561 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |