On binding sums of contact manifolds

2024/09/09 by Miguel Orbegozo Rodriguez, Rodriguez, Miguel Orbegozo
Engineering · Mathematics · #57K18 (57K20) #57K33 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2409.05612

openalex publication_date 2024/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we give examples of binding sums of contact 3-manifolds that do not preserve properties such as tightness or symplectic fillability. We also prove vanishing of the Heegaard Floer contact invariant for an infinite family of binding sums where the summands are Stein fillable. This recovers a result of Wendl and Latschev-Wendl. Along the way, we rectify a subtle computational error in a paper of Juhasz-Kang concerning the spectral order of a neighbourhood of a Giroux torsion domain.

Related

• Bordered contact invariants and half Giroux torsion
• A note on Stein fillings of contact manifolds
• Filtering the Heegaard Floer contact invariant
• Tight contact structures with no symplectic fillings
• Families of contact 3-manifolds with arbitrarily large Stein fillings