Obstruction Theory for Bigraded Differential Algebras

Abstract

We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted coefficients, as well as a proof of uniqueness. These results are further employed to study automorphism groups of minimal cbba's and to characterize formality in terms of grading automorphisms.

Our construction of minimal models does not produce connected models without the simply-connectedness assumption, [v2][v3] corrected this by adding the assumption. [v3] added a proof of that our inductive step in the construction of minimal models in fact terminates after applying the basic operation two times. 33 pages, comments welcome