Algebra Seminar 

18/01/2006, 11:00 — 12:00 — Room P3.10, Mathematics Building
Gustavo Granja, Instituto Superior Técnico

Realizing modules over the homology of a DGA

If $A$ is a DGA over a field and $X$ is a module over $H_{*}(A)$ one can ask whether $X=H_{*}(M)$ for some DG module $M$. If this is the case one says that $X$ is realizable. There are several obstruction theories to answer the question of realizability. I will explain the equivalence between four such obstruction theories, namely, between the obstructions to
(i) Finding an $A_{\infty }$ module structure on $X$,
(ii) Finding a Postnikov system for $X$ in the derived category of $A$-modules,
(iii) Realizing the simplicial bar resolution for $X$ in the category of $A$-modules,
(iv) Realizing the bar complex for $X$ in the category of $A$-modules.
Joint work with Sharon Hollander (Hebrew University).