Isomorphisms and peripheral structure of knot groups (Q1093951)
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scientific article; zbMATH DE number 4024304
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isomorphisms and peripheral structure of knot groups |
scientific article; zbMATH DE number 4024304 |
Statements
Isomorphisms and peripheral structure of knot groups (English)
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1988
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We show that every isomorphism of prime knot groups preserves the peripheral subgroups of the knot groups, and therefore every isomorphism of prime knot groups is induced by a homeomorphism of the knot manifolds by Waldhausen. We also show that a cable knot is invertible if and only if its companion is invertible.
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isomorphism of prime knot groups
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peripheral subgroups
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induced by a homeomorphism
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cable knot
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invertible
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companion
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