Title

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

Share

COinS