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Register a new user4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings
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We construct examples of smooth 4-dimensional manifolds M supporting a locally CAT(0)-metric, whose universal cover X satisfy Hruskas isolated flats condition, and contain 2-dimensional flats F with the property that the boundary at infinity of F defines a nontrivial knot in the boundary at infinity of X. As a consequence, we obtain that the fundamental group of M cannot be isomorphic to the fundamental group of any Riemannian manifold of nonpositive sectional curvature. In particular, M is a locally CAT(0)-manifold which does not support any Riemannian metric of nonpositive sectional curvature.
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