Abstract group actions of locally compact groups on CAT(0) spaces (Q2102719)
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scientific article; zbMATH DE number 7625252
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Abstract group actions of locally compact groups on CAT(0) spaces |
scientific article; zbMATH DE number 7625252 |
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Abstract group actions of locally compact groups on CAT(0) spaces (English)
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29 November 2022
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Summary: We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris-Nickolas for actions on trees. As a consequence we obtain a geometric proof for the fact that any abstract group homomorphism from a locally compact Hausdorff group into a torsion-free CAT(0) group is continuous.
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automatic continuity
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locally compact groups
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CAT(0) spaces
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