Smoothly parameterized Cech cohomology of complex manifolds

T Bailey, M Eastwood, S Gindikin

Research output: Contribution to journalArticlepeer-review

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.

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

Keywords

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

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