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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

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010)
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