Niebrzydowski Algebras and Trivalent Spatial Graphs

Paige Graves; Sam Nelson; Sherilyn Tamagawa

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arXiv · 1805.00104

Niebrzydowski Algebras and Trivalent Spatial Graphs

Paige Graves·Sam Nelson·Sherilyn Tamagawa

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Abstract

We introduce \textit{Niebrzydowski algebras}, algebraic structures with a ternary operation and a partially defined multiplication, with axioms motivated by the Reidemeister moves for $Y$-oriented trivalent spatial graphs and handlebody-links. As part of this definition, we identify generating sets of $Y$-oriented Reidemeister moves. We give some examples to demonstrate that the counting invariant can distinguish some $Y$-oriented trivalent spatial graphs and handlebody-links.

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Paige Graves, Sam Nelson, Sherilyn Tamagawa. 2018-04-30. Niebrzydowski Algebras and Trivalent Spatial Graphs. https://arxiv.org/abs/1805.00104

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