Regional knot invariants
Geometric Topology
2017-03-20 v1
Abstract
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 call 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 derive from the matrix just like the Alexander polynomial case.
Cite
@article{arxiv.1703.05869,
title = {Regional knot invariants},
author = {Zhiqing Yang},
journal= {arXiv preprint arXiv:1703.05869},
year = {2017}
}
Comments
10 pages, 6 figures