Examples of nonpolar limit spaces

In this paper we give an example showing that a limit space of manifolds with positive Ricci curvature can be nonpolar. Recall that a polar space is a space all of whose tangent cones have a pole at the origin. Polar limit spaces have many regularity properties. For instance, J. Cheeger and T. Colding have proven that the Hausdorff dimension of a polar limit space is an integer.