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.
Cite
@article{arxiv.2504.06590,
title = {Obstruction Theory for Bigraded Differential Algebras},
author = {Jiahao Hu},
journal= {arXiv preprint arXiv:2504.06590},
year = {2026}
}
Comments
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