6 papers
Knot-theoretic flocks
Maciej Niebrzydowski, Agata Pilitowska, Anna Zamojska-Dzienio
We characterize the para-associative ternary quasigroups (flocks) applicable to knot theory, and show which of these structures are isomorphic. We enumerate them up to order 64. We…
Layers of knot region colorings and higher differentials
Maciej Niebrzydowski
We inductively define layers of colorings of knot and knotted surface diagrams using ternary quasigroups. Homological invariants from such systems of colorings use shorter differen…
On a homology of ternary groups with applications to knot theory
Maciej Niebrzydowski
We define a homology for ternary groups using both associativity and skew elements. We describe the odd-even construction which yields many examples of ternary groups. We define th…
Knot-theoretic ternary groups
Maciej Niebrzydowski, Agata Pilitowska, Anna Zamojska-Dzienio
We describe various properties and give several characterizations of ternary groups satisfying two axioms derived from the third Reidemeister move in knot theory. Using special att…
Ternary quasigroups in knot theory
Maciej Niebrzydowski
We show that some ternary quasigroups appear naturally as invariants of classical links and links on surfaces. We also note how to obtain from them invariants of Yoshikawa moves. I…
Homology of ternary algebras yielding invariants of knots and knotted surfaces
Maciej Niebrzydowski
We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satis…