Trace Diagrams and Biquandle Brackets

Sam Nelson; Natsumi Oyamaguchi

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arXiv · 1705.07243

Trace Diagrams and Biquandle Brackets

Sam Nelson·Natsumi Oyamaguchi

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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.

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Sam Nelson, Natsumi Oyamaguchi. 2017-10-30. Trace Diagrams and Biquandle Brackets. https://arxiv.org/abs/1705.07243

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