arXiv subjects

Hamdi Kayaslan

Publications and source records attributed to Hamdi Kayaslan.

3 recordsLinked to original sources

arXiv2026

Persistent Homology of Biquandle Coloring Quivers

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, we obtain new invariants of links. We then introduce a quiver filtration-valued invariant of links induced by filtrations of biquandle endomorphism sets. We construct persistent homological invariants of links by applying persistence techniques to these quiver filtrations through the introduced homology theory.

math.GN↗

arXiv2025

Biquandle Virtual Brackets and Virtual Knotoids

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 bracket matrix, is a proper enhancement of the other invariants introduced in this paper.

math.AT↗

arXiv2025

Virtual Knotoids in Thickened Surfaces

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 knotoid theory. This gives a proof of a conjecture of Kauffman and the first author.

math.GT↗