Augmentation varieties and disk potentials I

Kenneth Blakey; Soham Chanda; Yuhan Sun; Chris T. Woodward

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arXiv · 2310.17821

Augmentation varieties and disk potentials I

Kenneth Blakey·Soham Chanda·Yuhan Sun·Chris T. Woodward

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Abstract

This is the first in a sequence of papers where we show that Lagrangian fillings such as the Harvey-Lawson filling in any dimension define augmentations of Chekanov-Eliashberg differential graded algebras by counting configurations of holomorphic disks connected by gradient trajectories, as in Aganagic-Ekholm-Ng-Vafa; we also prove that for Legendrian lifts of monotone tori, the augmentation variety is the zero level set of the Landau-Ginzburg potential of the Lagrangian projection, as suggested by Dimitroglou-Rizell-Golovko. In this part, we set up the foundations of moduli spaces of pseudoholomorphic buildings.

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BibTeX RIS

Kenneth Blakey, Soham Chanda, Yuhan Sun, Chris T. Woodward. 2026-01-01. Augmentation varieties and disk potentials I. https://arxiv.org/abs/2310.17821

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