6 papers · 1 filter
Distinguishing Power of 4-Legendrian Permutation Racks
Luc Ta, Peyton Phinehas Wood
We study 4-Legendrian racks and their effectiveness at distinguishing Legendrian knots. We prove that permutation racks with 4-Legendrian rack structures cannot distinguish Legendr…
Groups versus quandle-like invariants of 3-manifolds
Luc Ta
Risandles are nonassociative algebraic structures recently introduced to construct invariants of 3-manifolds. In this note, we show that the categories of groups and nonempty, fait…
Good involutions of twisted conjugation subquandles and Alexander quandles
Luc Ta
We completely describe good involutions of free quandles and subquandles of twisted conjugation quandles of groups, including all Alexander quandles. As an application, we enumerat…
Enumeration of virtual quandles up to isomorphism
Luc Ta
Virtual racks and virtual quandles are nonassociative algebraic structures based on the Reidemeister moves of virtual knots. In this note, we enumerate virtual dihedral quandles an…
Graph quandles: Generalized Cayley graphs of racks and right quasigroups
Luc Ta
This article lays the foundations for an analogue of geometric group theory that studies actions on graphs by right quasigroups, including racks and quandles. We study markings of…
Good involutions of conjugation subquandles
Luc Ta
Posed by Taniguchi, the classification of quandles with good involutions is a difficult question with applications to surface-knot theory. We address this question for subquandles…