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Abstract: This note describes sharp Milnor-Wood inequalities for the Euler number offlat oriented vector bundles over closed Riemannian manifolds locally isometricto products of hyperbolic planes. One consequence is that such manifolds do notadmit an affine structure, confirming Chern-Sullivan-s conjecture in thiscase. The manifolds under consideration are of particular interest, since incontrary to many other locally symmetric spaces they do admit flat vectorbundle of the corresponding dimension. When the manifold is irreducible and ofhigher rank, it is shown that flat oriented vector bundles are determinedcompletely by the sign of the Euler number.



Author: Michelle Bucher, Tsachik Gelander

Source: https://arxiv.org/







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