On the embedding complexity of Liouville manifolds

2020/12/08 by Sheel Ganatra, Ganatra, Sheel, Kyler Siegel +1 · 3 citations
Mathematics · #53Dxx #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2012.04627

openalex publication_date 2020/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Semi-global Kuranishi charts and the definition of contact homology
• Symplectic cohomology and Viterbo's theorem

Cited by

• Refined Elementary Capacities from Symplectic Field Theory
• Nonexistence of exact Lagrangian tori in affine conic bundles over ℂⁿ
• A landscape of contact manifolds via rational SFT
• The strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in ℝ⁴

Related

• Quantitative embedded contact homology
• Liouville hypersurfaces and connect sum cobordisms
• The contact Banach-Mazur distance and large scale geometry of overtwisted contact forms
• An L_∞ structure on symplectic cohomology
• Torus bundle Liouville domains are stably Weinstein