On the embedding complexity of Liouville manifolds

TL;DR

This paper introduces symplectic invariants based on contact homology to study and obstruct exact symplectic embeddings between Liouville manifolds, with applications to complex projective space divisors.

Contribution

It develops a new family of symplectic invariants using linearized contact homology and applies them to characterize embeddings in complex projective spaces.

Findings

Complete characterization of embeddings between divisor complements in many cases

Explicit embedding obstructions derived from pseudoholomorphic curves

Avoids Hamiltonian or virtual perturbations in proofs

Abstract

We define a family of symplectic invariants which obstruct exact symplectic embeddings between Liouville manifolds, using the general formalism of linearized contact homology and its L-infinity structure. As our primary application, we investigate embeddings between normal crossing divisor complements in complex projective space, giving a complete characterization in many cases. Our main embedding results are deduced explicitly from pseudoholomorphic curves, without appealing to Hamiltonian or virtual perturbations.