Model category structures on truncated multicomplexes for complex geometry
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917069912539136 |
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| author | Cirici, Joana Livernet, Muriel Whitehouse, Sarah |
| author_facet | Cirici, Joana Livernet, Muriel Whitehouse, Sarah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Model category structures on truncated multicomplexes for complex geometry Cirici, Joana Livernet, Muriel Whitehouse, Sarah Algebraic Topology Differential Geometry 18N40, 18G40, 32Q55 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. |
| title | Model category structures on truncated multicomplexes for complex geometry |
| topic | Algebraic Topology Differential Geometry 18N40, 18G40, 32Q55 |
| url | https://arxiv.org/abs/2501.13509 |