2023/12/04 by Daniel López Neumann, Roland van der Veen, Neumann, Daniel López +1
Mathematics · #20G42 #57K10 #57K16 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2312.02070
openalex publication_date 2023/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any simple complex Lie algebra \mathfrakg, we show that the degrees of the "ADO" link polynomials coming from the unrolled restricted quantum group UHq(\mathfrakg) at a root of unity give lower bounds to the Seifert genus of the link. We give a direct simple proof of this fact relying on a Seifert surface formula involving universal \mathfrakuq(\mathfrakg)-invariants, where \mathfrakuq(\mathfrakg) is the small quantum group. We give a second proof by showing that the invariant P_\mathfrakuq(\mathfrakb)θ(K) of our previous work coincides with such ADO invariants, where \mathfrakuq(\mathfrakb) is the Borel part of \mathfrakuq(\mathfrakg). To prove this, we show that equivariantizations of relative Drinfeld centers of crossed products essentially contain unrolled restricted quantum groups, a fact that could be of independent interest.