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Smoothly Parameterised Cech Cohomology of Complex Manifolds

Toby Bailey·Michael Eastwood·Simon Gindikin
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Abstract

A Stein covering of a complex manifold may be used to realise its analytic cohomology in accordance with the Cech theory. If, however, the Stein covering is parameterised 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.

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Toby Bailey, Michael Eastwood, Simon Gindikin. 2004-06-08. Smoothly Parameterised Cech Cohomology of Complex Manifolds. https://arxiv.org/abs/math/0406142

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