Cobordism maps in embedded contact homology
Abstract
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 Z / 2 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.
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