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Smoothly parameterized Cech cohomology of complex manifolds

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Original languageEnglish
Pages (from-to)923
Number of pages15
JournalJournal of Geometric Analysis
Volume15
Issue number1
Publication statusPublished - 2005

Abstract

A Stein covering of a complex manifold may be used to realize its analytic cohomology in accordance with the Cech theory. If, however, the Stein covering is parameterized by a smooth manifold rather than just a discrete set, then we construct a cohomology theory in which an exterior derivative replaces the usual combinatorial Cech differential. Our construction is motivated by integral geometry and the representation theory of Lie groups.

    Research areas

  • complex manifold, mixed manifold, Cech cohomology, PARTIAL-DERIVATIVE-COHOMOLOGY, HOLOMORPHIC REALIZATION, CO-HOMOLOGY, TRANSFORM, DOMAINS, SPACES

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