4-dimensional Locally Cat(0)-manifolds with No Riemannian Smoothings
نویسنده
چکیده
We construct examples of 4-dimensional manifolds M supporting a locally CAT(0)metric, whose universal covers Q M satisfy Hruska’s isolated flats condition, and contain 2-dimensional flats F with the property that @1F Š S ,! S Š @1 Q M are nontrivial knots. As a consequence, we obtain that the group 1.M/ cannot be isomorphic to the fundamental group of any compact Riemannian manifold of nonpositive sectional curvature. In particular, if K is any compact locally CAT(0)-manifold, then M K is a locally CAT(0)-manifold which does not support any Riemannian metric of nonpositive sectional curvature.
منابع مشابه
Commutative curvature operators over four-dimensional generalized symmetric spaces
Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.
متن کاملLarge Scale Detection of Half-flats in Cat(0) Spaces
Let M be a complete locally compact CAT(0)-space, and X an ultralimit of M . For γ ⊂M a k-dimensional flat, let γω be the k-dimensional flat in X obtained as an ultralimit of γ. In this paper, we identify various conditions on γω that are sufficient to ensure that γ bounds a (k + 1)-dimensional half-flat. As applications we obtain (1) constraints on the behavior of quasi-isometries between loca...
متن کاملEven- vs. Odd-dimensional Charney-Davis Conjecture
More than once we have heard that the Charney-Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dimensional spheres. A conjecture of Heinz Hopf asserts that the sign of the Euler characteristic of a smooth Riemannian 2d-dimensional manifold of non-positive sectional curvature is the same for all such manifolds, tha...
متن کاملGroups acting on CAT(0) cube complexes
We show that groups satisfying Kazhdan’s property (T) have no unbounded actions on nite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(−1) Riemannian manifold which is not homotopy equivalent to any nite dimensional, locally CAT(0) cube complex. AMS Classi cation numbers Primary: 20F32 Secondary: 20E42, 20G20
متن کاملX iv : g r - qc / 9 71 20 71 v 1 1 6 D ec 1 99 7 Riemannian Space - times of Gödel Type in Five Dimensions
The five-dimensional (5D) Riemannian Gödel-type manifolds are examined in light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by two essential parameters m 2 and ω : ...
متن کامل