Cantor sets in \(S^ 3\) with simply connected complements (Q1084705)
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scientific article; zbMATH DE number 3980030
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cantor sets in \(S^ 3\) with simply connected complements |
scientific article; zbMATH DE number 3980030 |
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Cantor sets in \(S^ 3\) with simply connected complements (English)
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1986
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The author gives a new example of a wild Cantor set in \(S^ 3\) with simply connected complement; it is ''defined by'' handlebodies of genus 2 and is simpler than the examples known previously. The author also gives two characterizations of tame Cantor sets: a Cantor set C in \(S^ 3\) is tame if and only if it satisfies at least one of the conditions: (a) every unknotted simple closed curve in \(S^ 3-C\) lies in the interior of a 3-disk in \(S^ 3-C\), (b) \(\pi_ 1(S^ 3-C-K)\) is finitely generated for each unknotted simple closed curve K in \(S^ 3-C\).
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wild Cantor set in \(S^ 3\) with simply connected complement
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tame Cantor sets
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