Geometry ``à la Gromov'' for the fundamental group of a closed 3- manifold \(M^ 3\) and the simple connectivity at infinity of \(\widetilde{M}^ 3\) (Q1317067)
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scientific article; zbMATH DE number 527444
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geometry ``à la Gromov'' for the fundamental group of a closed 3- manifold \(M^ 3\) and the simple connectivity at infinity of \(\widetilde{M}^ 3\) |
scientific article; zbMATH DE number 527444 |
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Geometry ``à la Gromov'' for the fundamental group of a closed 3- manifold \(M^ 3\) and the simple connectivity at infinity of \(\widetilde{M}^ 3\) (English)
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6 February 1996
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It is a well-known open question whether the universal cover of an irreducible aspherical closed 3-manifold \(M\) must be homeomorphic to \(R^3\). An algebraic version of this question asks whether the universal cover \(\widetilde {M}\) must be simply connected at infinity. This paper extends an idea of Casson on metric properties of Cayley graphs to investigate this algebraic question.
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universal cover of an irreducible aspherical closed 3-manifold
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simply connected at infinity
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metric properties of Cayley graphs
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