2025/01/23 by Joana Cirici, Cirici, Joana, Muriel Livernet +3
Mathematics · Physics and Astronomy · #18G40 #18N40 #32Q55 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · doi:10.48550/arxiv.2501.13509
openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 and generalized complex manifolds.