Abstract
We develop the theory of orbibundles from a geometrical viewpoint using diffeology. One of our goals is to present new tools allowing to calculate invariants of complex hyperbolic disc orbibundles over 2-orbifolds appearing in the geometry of 4-manifolds. These invariants are the Euler number of disc orbibundles and the Toledo invariant of PU(2,1)-representations of 2-orbifold groups.
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