Fibered links and unknotting operations (Q749923)

The paper is devoted to the investigation of Seifert surfaces for fibered links in rational homology 3-spheres. Let L be a fibered link in a rational homology 3-sphere M and let \(\chi\) (L) denotes the maximal Euler characteristic of Seifert surfaces for L. Suppose that \(L'\) is obtained from L by a single unknotting operation. The author proves that if \(\chi (L')>\chi (L)\), then there is a minimal genus Seifert surface S for L sucht that S is a plumbing of a surface and a Hopf band (the twisted annulus having the Hopf link on the boundary). For \(M=S^ 3\) this result was proved by \textit{M. Scharlemann} and \textit{A. Thompson} [Comment. Math. Helv. 64, No.4, 527-535 (1989; Zbl 0693.57004)]. More detailed investigations enabled the author to prove that among rational homology spheres only lens spaces contain unknotting number 1 fibered knots.