Realizing modules over the homology of a DGA |
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Authors: | Gustavo Granja Sharon Hollander |
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Institution: | a Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Tech. Univ. Lisbon, Portugal b Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel |
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Abstract: | Let A be a DGA over a field and X a module over H∗(A). Fix an A∞-structure on H∗(A) making it quasi-isomorphic to A. We construct an equivalence of categories between An+1-module structures on X and length n Postnikov systems in the derived category of A-modules based on the bar resolution of X. This implies that quasi-isomorphism classes of An-structures on X are in bijective correspondence with weak equivalence classes of rigidifications of the first n terms of the bar resolution of X to a complex of A-modules. The above equivalences of categories are compatible for different values of n. This implies that two obstruction theories for realizing X as the homology of an A-module coincide. |
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Keywords: | 55S35 55U15 16E45 |
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