an:04067876
Zbl 0654.57005
Scharlemann, Martin; Thompson, Abigail
Finding disjoint Seifert surfaces
EN
Bull. Lond. Math. Soc. 20, No. 1, 61-64 (1988).
00165855
1988
j
57M25
two orientable surfaces of minimal genus; Seifert surfaces of knots; knot; spanning surfaces
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.
L.Neuwirth