4 papers
Biquandle-Based Invariants of Virtual Knotoids and Connected Sum
Hamdi Kayaslan, Selçuk İlbeyli
In this paper, we study the behavior of biquandle-based invariants of virtual knotoids under their connected sum. We first show that the fundamental biquandle of the connected sum…
Persistent Homology of Biquandle Coloring Quivers
Hamdi Kayaslan
In this paper, we extend the notion of directed clique complex to quivers and introduce an associated homology theory. By applying this construction to biquandle coloring quivers,…
Biquandle Virtual Brackets and Virtual Knotoids
Neslihan Gügümcü, Hamdi Kayaslan
In this paper, we introduce invariants of virtual knotoids based on biquandles and biquandle virtual brackets. We show that one of these invariants, namely biquandle virtual bracke…
Virtual Knotoids in Thickened Surfaces
Neslihan Gügümcü, Hamdi Kayaslan
In this paper, we give a geometric interpretation of virtual knotoids as arcs in thickened surfaces. Then we show that virtual knotoid theory is a generalization of classical knoto…