Document Zbl 0628.57005

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Property P for the band-connect sum of two knots. (English) Zbl 0628.57005

Topology 26, 205-207 (1987).

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.

Reviewer: K.Murasugi

Cited in 2 Reviews

Cited in 5 Documents

MSC:

57M25

Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

band-sum of two knots; property P

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