Stallings twists which can be realized by plumbing and deplumbing Hopf bands

摘要

We define a type of Stallings twists, which represents a "complexity" of the twist, and show that the Stallings twists of a certain type on a fiber surface for a fibered link in S~3 can be realized by plumbing one Hopf band and deplumbing another Hopf band. Using this technique, we construct stable Hpf plumbings which are not Hpof plumbings with an arbitrary high first Betti number.