Towards a good definition of algebraically overtwisted

TL;DR

This paper establishes the equivalence of vanishing conditions across different symplectic field theory invariants, introducing the concept of algebraically overtwisted contact manifolds.

Contribution

It proves that the vanishing of contact homology, rational SFT, and full SFT are equivalent, defining a new class of algebraically overtwisted manifolds.

Findings

Vanishing of contact homology implies vanishing of rational SFT.

Vanishing of rational SFT implies vanishing of full SFT.

These vanishing conditions are equivalent for contact manifolds.

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".