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MiS Preprint
73/2001
Pathologies in Aleksandrov spaces of curvature bounded above
Valerii N. Berestovskii
Abstract
We construct in the paper two examples of Aleksandrov spaces A with curvature bounded above, which possess a pathological properties. In the first we give a CAT(-1)-space A, which is homeomorphic to $R^n , n\geq 5$, while its hyperbolic boundary in Gromov sense is not topological manifold. This construction is much simpler than in corresponding example of Davies-Januszkiewicz. In the second A has curvature $\leq 0$ and entropy dimension (around some point) strongly more than (equal) topological and Hausdorff dimensions.
