Glen T. Whitney | Searcharxiv

arXiv2020

Quandles with orbit series conditions

We introduce the notion of an orbit series in a quandle. Using this notion we define four families of quandles based on finiteness conditions on their orbit series. Intuitively, the classes tOS and tOSn correspond to finitary compositions of trivial quandles while the classes OS and OSn correspond to finitary compositions of connected quandles. We study properties of these four families of quandles and explore their relationships with several previously studied families of quandles: reductive, n-reductive, locally reductive, n-locally reductive, and solvable quandles.

math.GR↗

arXiv2018

On the Structure of Hom Quandles

We continue the study of the quandle of homomorphisms into a medial quandle begun in Crans and Nelson. We show that it suffices to consider only medial source quandles, and therefore the structure theorem of Jedlicka et al. provides a characterization of the Hom quandle. In the particular case when the target is 2-reductive this characterization takes on a simple form that makes it easy to count and determine the structure of the Hom quandle.

math.GT↗