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2025-11-26

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cc by (c) Joana Cirici et al., 2025
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/227067

Model category structures on truncated multicomplexes for complex geometry

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https://doi.org/10.1112/blms.70239

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 $N$-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.

Subject

Teoria espectral (Matemàtica), Teoria de l'homotopia, Espais analítics, Varietats complexes

Subject (English)

Spectral theory (Mathematics), Homotopy theory, Analytic spaces, Complex manifolds

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CIRICI, Joana, LIVERNET, Muriel and WHITEHOUSE, Sarah. Model category structures on truncated multicomplexes for complex geometry. Bulletin of the London Mathematical Society. 2025. Vol. 57, num. 12, pags. 4163-4177. ISSN 0024-6093. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/227067

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