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...
| Autores: | , |
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| 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) |
| 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. |
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