Analytic cohomology groups of infinite dimensional complex manifolds

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• 作者：Lá ; szló ; Lempert ^{lempert@purdue.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Analytic cohomology
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1428-1446
• 全文大小：464 K

文摘

Given a cohesive sheaf 35a02aa78c36fb7bcd012c2af517df" title="Click to view the MathML source">S$\mathcal{S}$ over a complex Banach manifold M  , we endow the cohomology groups H^q(M,S)$H^q(M,\mathcal{S})$ of M   and H^q(U,S)$H^q(\mathfrak{U},\mathcal{S})$ of open covers U$\mathfrak{U}$ of M   with a locally convex topology. Under certain assumptions we prove that the canonical map H^q(U,S)→H^q(M,S)$H^q(\mathfrak{U},\mathcal{S})\to H^q(M,\mathcal{S})$ is an isomorphism of topological vector spaces.