Calabi-Yau structures on topological Fukaya categories

Abstract

We develop a local-to-global formalism for constructing Calabi-Yau structures for global sections of constructible sheaves or cosheaves of categories. The required data - an isomorphism of the sheafified Hochschild homology with the topological dualizing sheaf - specializes to the classical notion of orientation when applied to the category of local systems on a manifold. We apply this construction to the cosheaves on arboreal skeleta arising in the microlocal approach to the A-model.

88 pages, 15 figures

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Cited by in corpus (9)

• Cluster varieties from Legendrian knots
• Relative Calabi-Yau structures
• Mirror symmetry for very affine hypersurfaces
• Derived coisotropic structures I: affine case
• Relative Calabi-Yau completions
• Homological mirror symmetry at large volume
• Calabi-Yau structures for multiplicative preprojective algebras
• Geometric and algebraic presentations of Weinstein domains
• Perverse Sheaves and Knot Contact Homology