Property P for the band-connect sum of two knots (Q1093210)
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scientific article; zbMATH DE number 4022164
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Property P for the band-connect sum of two knots |
scientific article; zbMATH DE number 4022164 |
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Property P for the band-connect sum of two knots (English)
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1987
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The author proves that the nontrivial band-sum of two knots has property P. This theorem implies immediately the affirmative solution to a long- standing conjecture (solved first by Scharlemann) that if a band-sum of two knots \(K_ 1\) and \(K_ 2\) is the unknot, then \(K_ 1\) and \(K_ 2\) are both the unknot and a band is also trivial. The proof of the theorem is short, but needs deep results due to D. Gabai.
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band-sum of two knots
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property P
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