Weak Relative Calabi-Yau Structures for Legendrian Contact Homology

Jiajie Ma; Joshua M. Sabloff

Weak Relative Calabi-Yau Structures for Legendrian Contact Homology

Symplectic Geometry 2025-09-03 v1

Authors: Jiajie Ma , Joshua M. Sabloff

Abstract

Legendrian Contact Homology (LCH) and its augmentations are important invariants of Legendrian submanifolds, and for Legendrian knots in the standard contact 3-space in particular. We increase understanding of the algebraic structure of LCH by generalizing the duality isomorphism and long exact sequence for linearized LCH for Legendrian knots to a weak relative Calabi-Yau structure for $A_\infty$ bimodules over the positive augmentation category.

Keywords

Legendrian Contact Homology weak relative Calabi-Yau structure $A_\infty$ bimodule augmentation category duality isomorphism

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@article{arxiv.2509.02485,
  title  = {Weak Relative Calabi-Yau Structures for Legendrian Contact Homology},
  author = {Jiajie Ma and Joshua M. Sabloff},
  journal= {arXiv preprint arXiv:2509.02485},
  year   = {2025}
}

Comments

69 pages, 23 figures

Weak Relative Calabi-Yau Structures for Legendrian Contact Homology

Abstract

Keywords

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