Open books supporting overtwisted contact structures and the Stallings twist
Open books supporting overtwisted contact structures and the Stallings twist
We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called "twisting loop". We show that the existence of a twisting loop on the fiber surface of an …