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Persistent Homology of Biquandle Coloring Quivers
Abstract
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.
Versions
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BibTeX
@misc{kayaslan2026persistent,
title = {{Persistent Homology of Biquandle Coloring Quivers}},
author = {Hamdi Kayaslan},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.14782},
eprint = {2605.14782},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.14782},
}
RIS
TY - UNPB
TI - Persistent Homology of Biquandle Coloring Quivers
AU - Hamdi Kayaslan
PY - 2026
DA - 2026/05/14
PB - arXiv
DO - 10.48550/arxiv.2605.14782
UR - https://arxiv.org/abs/2605.14782
AB - 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.
ER -