Skip to content
DraconiticResearch
Search Sources API
197,761 studies31 sourcesUpdated 46 min ago
PreprintarXiv licencearXiv

Biquandle Image Quivers

  • Geunyoung Kim
  • Sam Nelson
  • Puttipong Pongtanapaisan
Open at sourcePDFDOICite

Abstract

We introduce a new family of weighted quiver-valued invariants of oriented classical and virtual knots and link, surface-knots and surface-links, and immersed surface-knots and surface-links associated to finite biquandles. We derive several polynomial invariants from these quivers via decategorification. We provide examples to illustrate the computation of the invariant as well as toy examples showing tables of invariant values for small biquandles.

Related

  1. Persistent Homology of Biquandle Coloring Quivers
    Hamdi Kayaslan
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. An example of biquandle and an invariant of long virtual knots defined through it
    Nozomu Sekino
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Biquandle-Based Invariants of Virtual Knotoids and Connected Sum
    Hamdi Kayaslan, Selçuk İlbeyli
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsGeometry & topologyarXiv
  4. Quasimaps to Quivers with Potentials
    Yalong Cao, Gufang Zhao
    Memoirs of the American Mathematical SocietyPeer-reviewedLicence not statedFull text23 citedGeometry & topologyOpenAlex
  5. Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches
    Yaolong Shen, Changjian Su, Rui Xiong
    Communications in Mathematical PhysicsPeer-reviewedLicence not statedFull text14 citedGeometry & topologyOpenAlex

Cite

BibTeXRIS
BibTeX
@misc{kim2026biquandle,
  title = {{Biquandle Image Quivers}},
  author = {Geunyoung Kim and Sam Nelson and Puttipong Pongtanapaisan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25593},
  eprint = {2610.25593},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25593},
}
RIS
TY  - UNPB
TI  - Biquandle Image Quivers
AU  - Geunyoung Kim
AU  - Sam Nelson
AU  - Puttipong Pongtanapaisan
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25593
UR  - https://arxiv.org/abs/2610.25593
AB  - We introduce a new family of weighted quiver-valued invariants of oriented classical and virtual knots and link, surface-knots and surface-links, and immersed surface-knots and surface-links associated to finite biquandles. We derive several polynomial invariants from these quivers via decategorification. We provide examples to illustrate the computation of the invariant as well as toy examples showing tables of invariant values for small biquandles.
ER  -