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arXiv · 2609.26584

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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Vivek Shende, Wennan Zhang. 2026-09-22. Welschinger invariants and the Conway polynomial. https://arxiv.org/abs/2609.26584

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