2024/07/22 by Daniel López Neumann, Roland van der Veen, Neumann, Daniel López +1
Mathematics · Physics and Astronomy · #20G42 #57K10 #57K16 #Algebra over a field #FOS: Mathematics #Fibered knot #Geometric Topology (math.GT) #Mathematics #Physics #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum chaos and dynamical systems #Quantum mechanics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2407.15561
openalex publication_date 2024/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 S3, 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 S3 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.