Actions of finitely generated groups on the universal Menger curve (Q2759002)
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scientific article; zbMATH DE number 1680662
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Actions of finitely generated groups on the universal Menger curve |
scientific article; zbMATH DE number 1680662 |
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Actions of finitely generated groups on the universal Menger curve (English)
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10 December 2001
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homeomorphism group
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The author proves that every finitely generated group acts effectively on the universal Menger curve \(\mu_1.\) The proof starts from a \(3\)-manifold which collapses to the Cayley graph of the given group, applies to it the so-called Lefschetz construction to obtain a space which is at every point locally homeomorphic to \(\mu_1\) and then uses the fact that the end point compactification of this space is \(\mu_1.\)
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