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Model category structures on truncated multicomplexes for complex geometry

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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 complex manifolds.

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Bulletin of the London Mathematical Society, 2025, vol. 57, num.12, p. 4163-4177

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Model category structures on truncated multicomplexes for complex geometry