Trees,tight extensions of metric spaces,and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces |
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Authors: | Andreas WM Dress |
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Institution: | Mathematics Department, Universitat Bielefeld, Bielefeld 4800, West Germany |
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Abstract: | The concept of tight extensions of a metric space is introduced, the existence of an essentially unique maximal tight extension Tx—the “tight span,” being an abstract analogon of the convex hull—is established for any given metric space X and its properties are studied. Applications with respect to (1) the existence of embeddings of a metric space into trees, (2) optimal graphs realizing a metric space, and (3) the cohomological dimension of groups with specific length functions are discussed. |
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