On the embedding complexity of Liouville manifolds

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.

arXiv commentv3: various expository improvements and corrections

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Cited by in corpus (3)

• Counting curves with local tangency constraints
• Symplectic fillings of asymptotically dynamically convex manifolds II--$k$-dilations
• Nonexistence of exact Lagrangian tori in affine conic bundles over ${\mathbb{C}}^n$