Colored HOMFLYPT counts holomorphic curves

• 成果类型: Article
• 署名作者: Ekholm, Tobias; Shende, Vivek
• 署名单位: Uppsala University; Uppsala University; Royal Swedish Academy of Sciences; Mittag-Leffler Institute; University of Southern Denmark; University of California System; University of California Berkeley
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.2510118122
• 发表日期: 2025-12-16
• 页码: e2510118122
• 关键词: knot theory; gromov-witten theory; holomorphic curve; HOMFLYPT; idempotents; INVARIANTS; Duality; Algebra

摘要

Given a link in the three-sphere, its Lagrangian conormal can be transplanted to the resolved conifold, which is a certain noncompact Calabi-Yau threefold. Here we show that, as predicted by Ooguri and Vafa using string theoretic arguments, the count of all holomorphic curves in the resolved conifold ending on this Lagrangian is, appropriately understood, the collection of the HOMFLYPT invariants of all colorings of the link. This generalizes our previous work, Skeins on branes, arXiv:1901.08027, which identified a curve count that captures the uncolored case. The main ingredient in the present work is a skein-valued multiple cover formula for an isolated embedded annulus.