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PreprintarXiv licencearXiv

Welschinger invariants and the Conway polynomial

  • Vivek Shende
  • Wennan Zhang
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Abstract

Welschinger showed that counts of connected holomorphic disks with Lagrangian boundary in symplectic 6-manifolds, meeting at least one boundary constraint, can be made invariant by correcting them with counts of disconnected disks weighted by certain "self-linking" numbers. We show his invariant is the lowest order term in an all-genus curve count where curves are weighted by the Conway polynomials of their boundaries. This in turn is a specialization of the skein-valued curve count, but can be defined without the 4-chain and vector field used in that setup.

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Cite

BibTeXRIS
BibTeX
@misc{shende2026welschinger,
  title = {{Welschinger invariants and the Conway polynomial}},
  author = {Vivek Shende and Wennan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26584},
  eprint = {2609.26584},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26584},
}
RIS
TY  - UNPB
TI  - Welschinger invariants and the Conway polynomial
AU  - Vivek Shende
AU  - Wennan Zhang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26584
UR  - https://arxiv.org/abs/2609.26584
AB  - Welschinger showed that counts of connected holomorphic disks with Lagrangian boundary in symplectic 6-manifolds, meeting at least one boundary constraint, can be made invariant by correcting them with counts of disconnected disks weighted by certain "self-linking" numbers. We show his invariant is the lowest order term in an all-genus curve count where curves are weighted by the Conway polynomials of their boundaries. This in turn is a specialization of the skein-valued curve count, but can be defined without the 4-chain and vector field used in that setup.
ER  -