Deformation Theory of Differential Complexes

Deformations of differential complexes occur as a part of deformation theories of algebraic structures, but are interesting in their own right. In fact, this theory enjoys many properties that are ‘desirable’ but rare in other theories. We show (a) that the moduli space of deformations of a differential can be classified by a purely combinatorial object, namely, by monotone sequences in a countable poset, and (b) that the primary obstruction conjecture holds. This is the first category where this general conjecture of Gerstenhaber is proven to hold despite non-trivial obstructions. Our methods are elementary, but the result is not.