Preprint 73/2001

Pathologies in Aleksandrov spaces of curvature bounded above

Valerii N. Berestovskii

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Submission date: 01. Oct. 2001
Pages: 15
published in: Siberian advances in mathematics, 12 (2002) 4, p. 1-18 
with the following different title: Pathologies in Alexandrov spaces with curvature bounded above
MSC-Numbers: 53C23, 57Mxx, 52Bxx
Keywords and phrases: aleksandrov space eith curvature bounded above, hyperbolic boundary, topological dimension, hausdorff dimension, entropy dimension
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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 tex2html_wrap_inline12, 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 tex2html_wrap_inline16 and entropy dimension (around some point) strongly more than (equal) topological and Hausdorff dimensions.

24.11.2021, 02:11