Torsion and Open Book Decompositions

2009/09/18 by John B. Etnyre, Etnyre, John B., David Shea Vela–Vick +1
Computer Science · Mathematics · #57M27 #57R58 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems #Symplectic Geometry (math.SG) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0909.3465

openalex publication_date 2009/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if (B,π) is an open book decomposition of a contact 3-manifold (Y,ξ), then the complement of the binding B has no Giroux torsion. We also prove the sutured Heegaard-Floer c-bar invariant of the binding of an open book is non-zero.

Citations

• Holomorphic disks and topological invariants for closed three-manifolds
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• On the contact class in Heegaard Floer homology

Related

• Holomorphic Curves in Blown Up Open Books
• On the transverse invariant for bindings of open books
• Planar open book decompositions and contact structures
• Special moves for open book decompositions of 3-manifolds
• Planar open books and Floer homology