2010/01/23 by Chris Wendl, Wendl, Chris
Mathematics · #32Q65 #57R17 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematics and Applications #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1001.4109
openalex publication_date 2010/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use contact fiber sums of open book decompositions to define an infinite hierarchy of filling obstructions for contact 3-manifolds, called planar k-torsion for nonnegative integers k, all of which cause the contact invariant in Embedded Contact Homology to vanish. Planar 0-torsion is equivalent to overtwistedness, while every contact manifold with Giroux torsion also has planar 1-torsion, and we give examples of contact manifolds that have planar k-torsion for any k ≥ 2 but no Giroux torsion, leading to many new examples of nonfillable contact manifolds. We show also that the complement of the binding of a supporting open book never has planar torsion. The technical basis of these results is an existence and uniqueness theorem for J-holomorphic curves with positive ends approaching the (possibly blown up) binding of an ensemble of open book decompositions.