2018/11/23 by Leandro Vendramin, Vendramin, Leandro
Mathematics · #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Hopf algebra #Knot (papermaking) #Knot invariant #Knot polynomial #Knot theory #Mathematics #Physics #Pure mathematics #Quantum #Quantum invariant #Quantum mechanics #Topology (electrical circuits) #Yang–Baxter equation #math.GT
paper · pdf · doi:10.48550/arxiv.1811.09345
published in arXiv (Cornell University) (Cornell University) · 6 pages. An expository article written for an upcoming concise encyclopedia of knot theory
arxiv created 2018/11/23 · openalex publication_date 2018/11/23 · arxiv updated 2018/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The fundamental problem of knot theory is to know whether two knots are equivalent or not. As a tool to prove that two knots are different, mathematicians have developed various invariants. Knots invariants are just functions that can be computed from the knot and depend only on the topology of the knot. Here we describe quantum invariants, a powerful family of invariants related to the celebrated Yang-Baxter equation.