Trace Diagrams and Biquandle Brackets
Geometric Topology
2017-10-31 v2 Quantum Algebra
Abstract
We introduce a method of computing biquandle brackets of oriented knots and links using a type of decorated trivalent spatial graphs we call trace diagrams. We identify algebraic conditions on the biquandle bracket coefficients for moving strands over and under traces and identify a new stop condition for the recursive expansion. In the case of monochromatic crossings we show that biquandle brackets satisfy a Homflypt-style skein relation and we identify algebraic conditions on the biquandle bracket coefficients to allow pass-through trace moves.
Cite
@article{arxiv.1705.07243,
title = {Trace Diagrams and Biquandle Brackets},
author = {Sam Nelson and Natsumi Oyamaguchi},
journal= {arXiv preprint arXiv:1705.07243},
year = {2017}
}
Comments
22 pages; version 2 includes typo fixes. To appear in Int'l J. Math