2023/12/24 by Jonathan Trejos, Trejos, Jonathan
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2312.15374
openalex publication_date 2023/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We give a combinatorial description of the embedded contact complex (ECC) of a certain family of contact toric lens spaces that we call concave lens spaces. We also define a notion of a concave toric domain that generalizes the usual concave toric domain in a way that possesses a singularity point and has a boundary a lens space. After desingularization these toric domains include the unitary cotangent bundle of \mathbbS2 and the unitary cotangent bundle of ℝP2. We use the combinatorial expression of the ECC to compute the ECH capacities of these toric domains. Furthermore, for certain concave toric domains we describe a packing of symplectic manifolds that recovers their ECH capacities.