Analytic cohomology groups of infinite dimensional complex manifolds

2013/12/27 by Laszlo Lempert, Lempert, Laszlo
Mathematics · #32C35 #46E50 #58B12 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32C35 #msc:46E50 #msc:58B12

paper · pdf · doi:10.48550/arxiv.1312.7327

arxiv created 2013/12/27 · arxiv updated 2013/12/30

Abstract

Given a cohesive sheaf \Cal S over a complex Banach manifold M, we endow the cohomology groups H^q(M,\Cal S) of M and H^q(\frak U,\Cal S) of open covers \frak U of M with a locally convex topology. Under certain assumptions we prove that the canonical map H^q(\frak U,\Cal S)→ H^q(M,\Cal S) is an isomorphism of topological vector spaces.

Related

• Representing analytic cohomology groups of complex manifolds
• Analytic cohomology in a Banach space
• Smoothly Parameterised Cech Cohomology of Complex Manifolds
• On the cohomology groups of holomorphic Banach bundles
• Continuous group cohomology with coefficients in locally analytic vectors of admissible ℚ_p -Banach space representations