Biquandle Knot Invariants

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Papers and Presentations

The Structure of Biquandle Brackets
Paper (published in the Journal of Knot Theory and its Ramifications), JKTR DOI, on the arXiv.
Poster (presented at the Young Mathematicians Conference, 2018).

Categorifying Biquandle Brackets
Paper (submitted to the Journal of Knot Theory and its Ramifications), on the arXiv.
My honors thesis at OSU (simplified version of above paper, includes Mathematica package documentation).
Slides (presented at the Young Mathematicians Conference, 2019), on Sergei Chmutov's webiste.
Poster (presented at the Joint Mathematics Meetings, 2020).

Mathematica Packages

Biquandles.wl
BiquandleBrackets.wl
Biquandle2Cocycles.wl
BiquandleBracketCanonical2Cocycle.wl

Conjectures and Questions

1: If \(X\) is a biquandle and \(\beta\) is a biquandle bracket over \(X\), then \(\beta\) is still a biquandle bracket over the trivial biquandle on the underlying set of \(X\).
2: How does the biquandle homology invariant \(\operatorname{Bh}_\beta\) compare to the biquandle bracket invariant \(\Phi_X^\beta\)?
3: Does a true Khovanov homology-style categorification of the biquandle bracket exist?