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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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 |
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doaj-fac691b7b963485eb6091e61c87f961a2020-11-25T02:12:28ZengDe GruyterComplex Manifolds2300-74432019-01-016122826410.1515/coma-2019-0012coma-2019-0012Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifoldsYagisita Hiroki0Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto-City, 603-8555, JapanLet 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.http://www.degruyter.com/view/j/coma.2019.6.issue-1/coma-2019-0012/coma-2019-0012.xml?format=INTtopological deformation of complex analytic structuresinfinite-dimensional manifoldcommutative c*-algebraserre-swan theorem19l9932q9946j9958b99 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yagisita Hiroki |
| spellingShingle |
Yagisita Hiroki Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds Complex Manifolds topological deformation of complex analytic structures infinite-dimensional manifold commutative c*-algebra serre-swan theorem 19l99 32q99 46j99 58b99 |
| author_facet |
Yagisita Hiroki |
| author_sort |
Yagisita Hiroki |
| title |
Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds |
| title_short |
Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds |
| title_full |
Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds |
| title_fullStr |
Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds |
| title_full_unstemmed |
Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds |
| title_sort |
finite-dimensional complex manifolds on commutative banach algebras and continuous families of compact complex manifolds |
| publisher |
De Gruyter |
| series |
Complex Manifolds |
| issn |
2300-7443 |
| publishDate |
2019-01-01 |
| description |
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. |
| topic |
topological deformation of complex analytic structures infinite-dimensional manifold commutative c*-algebra serre-swan theorem 19l99 32q99 46j99 58b99 |
| url |
http://www.degruyter.com/view/j/coma.2019.6.issue-1/coma-2019-0012/coma-2019-0012.xml?format=INT |
| work_keys_str_mv |
AT yagisitahiroki finitedimensionalcomplexmanifoldsoncommutativebanachalgebrasandcontinuousfamiliesofcompactcomplexmanifolds |
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1724909087631605760 |