2017/05/20 by Nelson, Sam, Oyamaguchi, Natsumi · 2 citations
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1705.07243
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.