Filtered 𝐴-infinity structures in complex geometry

Cirici, Joana; Sopena-Gilboy, Anna

doi:10.1090/proc/16009

Filtered $A$-infinity structures in complex geometry
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by Joana Cirici and Anna Sopena-Gilboy PDF

Proc. Amer. Math. Soc. 150 (2022), 4067-4082 Request permission

Abstract:

We prove a filtered version of the Homotopy Transfer Theorem which gives an $A$-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the geometry and topology of complex manifolds, using the Hodge filtration, as well as to complex algebraic varieties, using mixed Hodge theory.

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