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On the cohomology and geometry of principal sheeaves

Vassiliou E.

Demonstratio Mathematica

2003

Vol. 36, nr 2

289--306

We study the cohomological classification of principal sheaves, the latter being defined in a slightly different way than in [6], a fact allowing to consider on them geometrical objects like connections. The classification of vector sheaves (studied in [10]) is now a corollary of the classification of their principal sheaves of frames. In particular, principal sheaves with an abelian structural sheaf, equipped (the former) with a connection, admit a hypercohomological classification generalizing that of Maxwell fields given in [10].