2019/12/02 by Jacob Hunter Rooney, Rooney, Jacob · 1 citation
Computer Science · Mathematics · #53D42 #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1912.01048
openalex publication_date 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an exact symplectic cobordism (X, λ) between contact 3-manifolds (Y+, λ+) and (Y-, λ-) with no elliptic Reeb orbits up to a certain action, we define a chain map from the embedded contact homology (ECH) chain complex of (Y+, λ+) to that of (Y-, λ-), both taken with coefficients in \mathbb Z / 2 \mathbb Z. The map is defined by counting punctured holomorphic curves with ECH index 0 in the completion of the cobordism and new objects that we call ECH buildings, answering a question of Hutchings.