Quasi-trivial Quandles and Biquandles, Cocycle Enhancements and Link-Homotopy of Pretzel links

Mohamed Elhamdadi; Minghui Liu; Sam Nelson

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arXiv · 1704.01224

Quasi-trivial Quandles and Biquandles, Cocycle Enhancements and Link-Homotopy of Pretzel links

Mohamed Elhamdadi·Minghui Liu·Sam Nelson

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Abstract

We investigate some algebraic structures called quasi-trivial quandles and we use them to study link-homotopy of pretzel links. Precisely, a necessary and sufficient condition for a pretzel link with at least two components being trivial under link-homotopy is given. We also generalize the quasi-trivial quandle idea to the case of biquandles and consider enhancement of the quasi-trivial biquandle cocycle counting invariant by quasi-trivial biquandle cocycles, obtaining invariants of link-homotopy type of links analogous to the quasi-trivial quandle cocycle invariants in Ayumu Inoue's article arXiv:1205.5891.

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Mohamed Elhamdadi, Minghui Liu, Sam Nelson. 2017-04-05. Quasi-trivial Quandles and Biquandles, Cocycle Enhancements and Link-Homotopy of Pretzel links. https://arxiv.org/abs/1704.01224

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