3 papers
math.GN2026
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,…
math.GT2026
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…
math.AT2025
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…