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arXiv · 1912.01048

Cobordism maps in embedded contact homology

Jacob Rooney
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Abstract

Given an exact symplectic cobordism $(X, \lambda)$ between contact $3$-manifolds $(Y_+, \lambda_+)$ and $(Y_-, \lambda_-)$ with no elliptic Reeb orbits up to a certain action, we define a chain map from the embedded contact homology (ECH) chain complex of $(Y_+, \lambda_+)$ to that of $(Y_-, \lambda_-)$, 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.

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Jacob Rooney. 2019-12-02. Cobordism maps in embedded contact homology. https://arxiv.org/abs/1912.01048

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