Cohomology of minimal Sullivan algebras of non-finite type and their realizations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910619024752640 |
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| author | Zhou, Jiawei |
| author_facet | Zhou, Jiawei |
| contents | We prove that the morphisms from a minimal Sullivan algebra $ΛV$ to $A_{PL}(|ΛV|)$, the algebra of polynomial differential forms on its realization, can be quasi-isomorphic if and only if the cohomology $H(ΛV)$ is of finite type. Importantly, $ΛV$ itself need not be of finite type. For example, it can be the minimal Sullivan model of the wedge sum of a circle and a sphere. This provides a negative answer to a question posed by Félix, Halperin, and Thomas. Furthermore, we study the spaces whose homotopy groups are reflected by their minimal Sullivan models as a generalization of Sullivan spaces, and explore which properties of Sullivan spaces can be broadened. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology of minimal Sullivan algebras of non-finite type and their realizations Zhou, Jiawei Algebraic Topology We prove that the morphisms from a minimal Sullivan algebra $ΛV$ to $A_{PL}(|ΛV|)$, the algebra of polynomial differential forms on its realization, can be quasi-isomorphic if and only if the cohomology $H(ΛV)$ is of finite type. Importantly, $ΛV$ itself need not be of finite type. For example, it can be the minimal Sullivan model of the wedge sum of a circle and a sphere. This provides a negative answer to a question posed by Félix, Halperin, and Thomas. Furthermore, we study the spaces whose homotopy groups are reflected by their minimal Sullivan models as a generalization of Sullivan spaces, and explore which properties of Sullivan spaces can be broadened. |
| title | Cohomology of minimal Sullivan algebras of non-finite type and their realizations |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2407.20881 |