Quasi-Trivial Quandles and Biquandles, Cocycle Enhancements and Link-Homotopy of Pretzel Links
Document Type
Article
Publication Date
2018
Keywords
Quasi-trivial, quandle, biquandle, cocycle, pretzel links
Digital Object Identifier (DOI)
https://doi.org/10.1142/S0218216518430071
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 Inoue’s paper
Was this content written or created while at USF?
Yes
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.
https://digitalcommons.usf.edu/mth_facpub/102
