2016/10/30 by Jiro Adachi, Adachi, Jiro
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT
paper · pdf · doi:10.48550/arxiv.1610.09672
arxiv created 2016/10/30 · openalex publication_date 2016/10/30 · arxiv updated 2016/11/01 · openalex created_date 2016/11/11 · openalex updated_date 2026/07/28
Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the 3-dimensional Lutz twists are introduced. One of the operations makes a contact manifold overtwisted in any dimension. Another one makes it weakly symplectically non-fillable. And the other one makes it strongly symplectically non-fillable. In other words, they make the overtwisted disc, the bordered Legendrian open books, and the Giroux domains, respectively. The first two modifications can be realized by sequences of contact round surgeries. The first operation can be applied anywhere of any contact manifold easily. Further, a version of the first operation keeps the homotopy classes of contact structures as almost contact structures, and the other version contributes to the Euler classes of contact structures.