On the rank of amalgamated products and product knot groups (Q1298115)
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scientific article; zbMATH DE number 1336966
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rank of amalgamated products and product knot groups |
scientific article; zbMATH DE number 1336966 |
Statements
On the rank of amalgamated products and product knot groups (English)
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1 December 1999
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We show that the rank of an amalgamated product of \(n\) factors is at least \(n+1\) if the amalgam satisfies a condition which is slightly weaker than malnormality. As an application, we prove that the rank of the group of a knot which is the connected sum of \(n\) knots is at least \(n+1\). The proofs are based on the Nielsen method in amalgamated products.
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rank of amalgamated products
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product knot groups
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connected sums of knots
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malnormality
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