Smoothly parameterized Čech cohomology of complex manifolds | Zendy

Toby N. Bailey | Zendy; Michael Eastwood | Zendy; Simon Gindikin | Zendy

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Smoothly parameterized Čech cohomology of complex manifolds

Author(s) -

Toby N. Bailey,

Michael Eastwood,

Simon Gindikin

Publication year - 2005

Publication title -

journal of geometric analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.156

H-Index - 47

eISSN - 1559-002X

pISSN - 1050-6926

DOI - 10.1007/bf02921856

Subject(s) - mathematics , cohomology , parameterized complexity , manifold (fluid mechanics) , pure mathematics , differential geometry , differential form , de rham cohomology , algebra over a field , differential (mechanical device) , topology (electrical circuits) , equivariant cohomology , combinatorics , physics , mechanical engineering , engineering , thermodynamics

A Stein covering of a complex manifold may be used to realize its analytic cohomology in accordance with the Čech 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.

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