2013/07/22 by Atsushi Ishii, Ishii, Atsushi, Akira Masuoka +1
Mathematics · #57M27 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M27
paper · pdf · doi:10.48550/arxiv.1307.5632
25 Pages
arxiv created 2013/07/22 · openalex publication_date 2013/07/22 · arxiv updated 2013/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A handlebody-knot is a handlebody embedded in the 3-sphere. We establish a uniform method to construct invariants for handlebody-links. We introduce the category T of handlebody-tangles and present it by generators and relations. The result tells us that every functor on T that gives rise to invariants is derived from what we call a quantum-commutative quantum-symmetric algebra in the target category. The example of such algebras of our main concern is finite-dimensional unimodular Hopf algebras. We investigate how those Hopf algebras give rise to handlebody-knot invariants.