Quasi-Trivial Quandles and Biquandles, Cocycle Enhancements and Link-Homotopy of Pretzel Links
Quasi-trivial, quandle, biquandle, cocycle, pretzel links
Digital Object Identifier (DOI)
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 Inoue’s paper
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Citation / Publisher Attribution
Journal of Knot Theory and Its Ramifications, v. 27, issue 11, art. 1843007
Scholar Commons Citation
Elhamdadi, Mohamed; Liu, Minghui; and Nelson, Sam, "Quasi-Trivial Quandles and Biquandles, Cocycle Enhancements and Link-Homotopy of Pretzel Links" (2018). Mathematics and Statistics Faculty Publications. 102.