Model category structures on truncated multicomplexes for complex geometry

Abstract To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to ‐multicomplexes. We present a family of model category structures on the category of ‐multicomplexes where the weak equivalences are the morphisms inducing a quasi‐isomorphism at a fixed page of the first spectral sequence and at a fixed page of the second spectral sequence. Such weak equivalences arise naturally in complex geometry. In particular, the model structures presented here establish a basis for studying homotopy types of almost complex manifolds.