2017/02/17 by Zhiqing Yang
Mathematics · #Advanced Combinatorial Mathematics #Alexander polynomial #Algebraic Geometry and Number Theory #Bracket polynomial #Geometric and Algebraic Topology #Invariant (physics) #Jones polynomial #Knot (papermaking) #Knot invariant #Knot polynomial #Knot theory #Quantum invariant #math.GT #msc:57M25 #msc:57M27
paper · pdf · doi:10.1142/s0218216517420068
10 pages, 6 figures
openalex publication_date 2017/02/17 · openalex created_date 2017/02/24 · arxiv created 2017/03/17 · arxiv updated 2017/03/20 · openalex updated_date 2026/08/05
In this paper, a regional knot invariant is constructed. Like the Wirtinger presentation of a knot group, each planar region contributes a generator, and each crossing contributes a relation. The invariant is called a tridle of the link. As in the quandle theory, one can define Alexander quandle and get Alexander polynomial from it. For link diagram, one can also define a linear tridle and its presentation matrix. A polynomial invariant can be derived from the matrix just like the Alexander polynomial case.