Persistent Homology of Biquandle Coloring Quivers
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917495737155584 |
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| author | Kayaslan, Hamdi |
| author_facet | Kayaslan, Hamdi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14782 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Persistent Homology of Biquandle Coloring Quivers Kayaslan, Hamdi General Topology 57K12, 55N31 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. |
| title | Persistent Homology of Biquandle Coloring Quivers |
| topic | General Topology 57K12, 55N31 |
| url | https://arxiv.org/abs/2605.14782 |