2006/08/15 by Ryosuke Yamamoto, Yamamoto, Ryosuke
Engineering · Mathematics · #57M25 #57M50 #57R17 #Advanced Materials and Mechanics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Modular Robots and Swarm Intelligence
paper · pdf · doi:10.48550/arxiv.math/0608371
openalex publication_date 2006/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 open book is equivalent up to positive stabilization to the existence of an overtwisted disk in the contact manifold supported by the open book. We also show a criterion for overtwistedness using a certain arc properly embedded in the fiber surface, which is an extension of Goodman's one.