Finding disjoint Seifert surfaces. (English) Zbl 0654.57005

The authors prove that given two orientable surfaces S, T of minimal genus, spanning a tubular neighborhood of a knot K, there is a sequence of surfaces \(S=S_ 0,S_ 1,S_ 2...S_{n-1},S_ n=T\), such that \(S_ i\) and \(S_{i-1}\) are disjoint, and the \(S_ i\) are spanning surfaces of minimal genus for K. It was not previously known that the intervening surfaces could be all of minimal genus.
They also show there is a sequence of spanning surfaces starting with an arbitrary orientable surface, ending with a surface of minimal genus, and with each successive surface of lesser genus than and disjoint from the preceding.
Reviewer: L.Neuwirth


57M25 Knots and links in the \(3\)-sphere (MSC2010)
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