Towards a good definition of algebraically overtwisted

Abstract

Symplectic field theory (SFT) is a collection of homology theories that provide invariants for contact manifolds. We give a proof that vanishing of any one of either contact homology, rational SFT or (full) SFT are equivalent. We call a manifold for which these theories vanish "algebraically overtwisted".

9 pages; improved description of SFT, simplified proof, added marked points in main theorem

References in corpus (4)

• Compactness results in Symplectic Field Theory
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Vanishing of the contact homology of overtwisted contact 3--manifolds
• Polyfolds And A General Fredholm Theory

Cited by in corpus (7)

• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• Algebraic Torsion in Contact Manifolds
• First steps in stable Hamiltonian topology
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• No homotopy 4-sphere invariants using ECH = SWF
• Taubes's proof of the Weinstein conjecture in dimension three
• A landscape of contact manifolds via rational SFT