4 papers
Biquandle Arrow Weight Quiver Representations
Sam Nelson, Migiwa Sakurai
We define an infinite family of quiver representation-valued invariants of classical and virtual knots associated to a choice of data vector consisting of a biquandle, abelian grou…
Categorification of Biquandle Arrow Weight Invariants via Quivers
Sam Nelson, Migiwa Sakurai
Introduced in arXiv:2211.12606, biquandle arrow weight invariants are enhancements of the biquandle counting invariant for oriented virtual and classical knots defined from biquand…
On -trivialities of classical and virtual knots for some unknotting operations
Noboru Ito, Migiwa Sakurai
In this paper, we introduce a new nontrivial filtration, called F-order, for classical and virtual knot invariants; this filtration produces filtered knot invariants, which are cal…
Higher-order finite type invariants of classical and virtual knots and unknotting operations
Noboru Ito, Migiwa Sakurai
Vassiliev introduced filtered invariants of knots using an unknotting operation, called crossing changes. Goussarov, Polyak, and Viro introduced other filtered invariants of virtua…