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PreprintCC BY 4.0arXiv

Worldsheet skeins and block decomposition of quivers

  • Sachin Chauhan
  • Piotr Kucharski
  • Lukas Nakamura
  • Dmitry Noshchenko
  • Ramadevi Pichai
  • Vivek Kumar Singh
  • Marko Stošić
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Abstract

Following the knot-quiver correspondence, we investigate quiver counterparts of the HOMFLYPT skein relations by interpreting link invariants in terms of holomorphic worldsheets and their multicover contributions. Extending this framework to more general worldsheet geometries, we conjecture that, up to quiver equivalence, the adjacency matrix of the quiver associated with any link in a skein triple admits a block decomposition whose diagonal blocks are quiver adjacency matrices associated with the other two links. We verify this conjecture in numerous examples.

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Cite

BibTeXRIS
BibTeX
@misc{chauhan2026worldsheet,
  title = {{Worldsheet skeins and block decomposition of quivers}},
  author = {Sachin Chauhan and Piotr Kucharski and Lukas Nakamura and Dmitry Noshchenko and Ramadevi Pichai and Vivek Kumar Singh and Marko Stošić},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07455},
  eprint = {2611.07455},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07455},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Worldsheet skeins and block decomposition of quivers
AU  - Sachin Chauhan
AU  - Piotr Kucharski
AU  - Lukas Nakamura
AU  - Dmitry Noshchenko
AU  - Ramadevi Pichai
AU  - Vivek Kumar Singh
AU  - Marko Stošić
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07455
UR  - https://arxiv.org/abs/2611.07455
AB  - Following the knot-quiver correspondence, we investigate quiver counterparts of the HOMFLYPT skein relations by interpreting link invariants in terms of holomorphic worldsheets and their multicover contributions. Extending this framework to more general worldsheet geometries, we conjecture that, up to quiver equivalence, the adjacency matrix of the quiver associated with any link in a skein triple admits a block decomposition whose diagonal blocks are quiver adjacency matrices associated with the other two links. We verify this conjecture in numerous examples.
ER  -