Filtered A-infinity structures in complex geometry

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 fi...

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Detalles Bibliográficos
Autores: Cirici, Joana, Sopena Gilboy, Anna
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/191978
Acceso en línea:https://hdl.handle.net/2445/191978
Access Level:acceso abierto
Palabra clave:Teoria de l'homotopia
Geometria diferencial
Teoria de Hodge
Singularitats (Matemàtica)
Homotopy theory
Differential geometry
Hodge theory
Singularities (Mathematics)
Descripción
Sumario: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.