On the embedding complexity of Liouville manifolds

Using the formalism of L-infinity structures in linearized contact homology, we introduce new numerical "complexity" invariants of a Liouville manifold which obstruct Liouville embeddings. As an application, we give at many times complete characterizations of Liouville embeddings between normal crossing divisor complements in complex projective space. The main embedding results are deduced explicitly from pseudoholomorphic curves (of genus 0 with many positive ends) without appealing to Hamiltonian or virtual perturbations. This is joint work with Kyler Siegel.