Formulae in noncommutative Hodge theory

Abstract

We prove that the cyclic homology of a saturated $A_{\infty }$ category admits the structure of a `polarized variation of Hodge structures', building heavily on the work of many authors: the main point of the paper is to present complete proofs, and also explicit formulae for all of the relevant structures. This forms part of a project of Ganatra, Perutz and the author, to prove that homological mirror symmetry implies enumerative mirror symmetry.

42 pages, 5 figures; some material removed, expository changes

References in corpus (1)

• Tensor product of filtered $A_{\infty }$-algebras

Cited by in corpus (5)

• Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures
• Categorical primitive forms of Calabi-Yau $A_{\infty }$-categories with semi-simple cohomology
• Versality of the relative Fukaya category
• The cyclic open-closed map, u-connections and R-matrices
• Open Gromov-Witten invariants from the Fukaya category