Realizing modules over the homology of a DGA
| dc.creator | Granja, Gustavo | |
| dc.creator | Hollander, Sharon | |
| dc.date | 2007-08-16 | |
| dc.date.accessioned | 2026-07-07T08:23:56Z | |
| dc.date.available | 2026-07-07T08:23:56Z | |
| dc.description | Let A be a DGA over a field and X a module over H_*(A). Fix an $A_\infty$-structure on H_*(A) making it quasi-isomorphic to A. We construct an equivalence of categories between A_{n+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 A_n-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. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0708.2235 | |
| dc.identifier | http://arxiv.org/abs/0708.2235 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136177 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Rings and Algebras | |
| dc.subject | 55S35, 55U15, 16E45 | |
| dc.title | Realizing modules over the homology of a DGA | |
| dc.type | text |