Actions of discrete groups on nonpositively curved spaces (Q1817309)
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scientific article; zbMATH DE number 952634
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Actions of discrete groups on nonpositively curved spaces |
scientific article; zbMATH DE number 952634 |
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Actions of discrete groups on nonpositively curved spaces (English)
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12 February 1997
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This note contains several observations concerning discrete groups of non-parabolic isometries of spaces of nonpositive curvature. We prove that (almost all) surface mapping class groups do not admit such actions; in particular, they do not act cocompactly. A new obstruction to the existence of a nonpositively curved metric on closed manifolds is presented. We give examples of 4-manifolds fibered over surfaces and of graph 3-manifolds fibered over the circle which do not admit metrics of nonpositive curvature.
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groups of isometries
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mapping class groups
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actions
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nonpositively curved metrics
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closed manifolds
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