"Obstructions to Riemannian smoothing of non-positively curved manifolds"
Sathaye, BakulIn this talk I will discuss obstructions to having a smooth Riemannian metric with non-positive sectional curvature on a locally CAT(0) manifold. I will briefly discuss a knotting obstruction in dimension 4 and explain why this obstruction does not work in higher dimensions. I will then discuss a large scale quasi-isometry invariant of pairs of spaces (X, Y) called the 'fundamental group of the Y-end' and show how it can be used to give a coarse knotting obstruction to Riemannian smoothings in higher dimensions. This is joint work with Jean-Francois Lafont.