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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Autor principal:	Yagisita Hiroki
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2019
Materias:	topological deformation of complex analytic structures infinite-dimensional manifold commutative c*-algebra serre-swan theorem 19l99 32q99 46j99 58b99 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/fac691b7b963485eb6091e61c87f961a
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id	oai:doaj.org-article:fac691b7b963485eb6091e61c87f961a
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spelling	oai:doaj.org-article:fac691b7b963485eb6091e61c87f961a2021-12-02T10:44:17ZFinite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds2300-744310.1515/coma-2019-0012https://doaj.org/article/fac691b7b963485eb6091e61c87f961a2019-01-01T00:00:00Zhttp://www.degruyter.com/view/j/coma.2019.6.issue-1/coma-2019-0012/coma-2019-0012.xml?format=INThttps://doaj.org/toc/2300-7443Let 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.Yagisita HirokiDe Gruyterarticletopological deformation of complex analytic structuresinfinite-dimensional manifoldcommutative c*-algebraserre-swan theorem19l9932q9946j9958b99MathematicsQA1-939ENComplex Manifolds, Vol 6, Iss 1, Pp 228-264 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	topological deformation of complex analytic structures infinite-dimensional manifold commutative c*-algebra serre-swan theorem 19l99 32q99 46j99 58b99 Mathematics QA1-939
spellingShingle	topological deformation of complex analytic structures infinite-dimensional manifold commutative c*-algebra serre-swan theorem 19l99 32q99 46j99 58b99 Mathematics QA1-939 Yagisita Hiroki Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds
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.
format	article
author	Yagisita Hiroki
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
publishDate	2019
url	https://doaj.org/article/fac691b7b963485eb6091e61c87f961a
work_keys_str_mv	AT yagisitahiroki finitedimensionalcomplexmanifoldsoncommutativebanachalgebrasandcontinuousfamiliesofcompactcomplexmanifolds
_version_	1718396804772397056

Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds

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