Cirici, JoanaLivernet, MurielWhitehouse, Sarah2026-02-192026-02-192025-11-260024-6093https://hdl.handle.net/2445/227067To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to $N$-multicomplexes. We present a family of model category structures on the category of $N$-multicomplexes where the weak equivalences are the morphisms inducing a quasi-isomorphism at a fixed page $r$ of the first spectral sequence and at a fixed page $s$ 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.15 p.application/pdfengcc by (c) Joana Cirici et al., 2025http://creativecommons.org/licenses/by/4.0/Teoria espectral (Matemàtica)Teoria de l'homotopiaEspais analíticsVarietats complexesSpectral theory (Mathematics)Homotopy theoryAnalytic spacesComplex manifoldsinfo:eu-repo/semantics/article7656612026-02-19info:eu-repo/semantics/openAccess