Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds
Let Γ(M) be the set of all global continuous cross sections of a continuous family M of compact complex manifolds on a compact Hausdorff space X. In this paper, we introduce a C(X)-manifold structure on Γ(M). Especially, if X is contractible, then Γ(M) is a finite-dimensional C(X)-manifold. Here, C(...
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-01-01
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| Series: | Complex Manifolds |
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| Online Access: | http://www.degruyter.com/view/j/coma.2019.6.issue-1/coma-2019-0012/coma-2019-0012.xml?format=INT |
| Summary: | Let Γ(M) be the set of all global continuous cross sections of a continuous family M of compact complex manifolds on a compact Hausdorff space X. In this paper, we introduce a C(X)-manifold structure on Γ(M). Especially, if X is contractible, then Γ(M) is a finite-dimensional C(X)-manifold. Here, C(X) denotes the Banach algebra of all complex-valued continuous functions on X. |
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| ISSN: | 2300-7443 |