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Title:
From ECH to HF: The Story You Have Never Heard
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Abstract:
After describing definitions of \widehat{HF} and \widehat{ECH} adapted to open book decompositions, I will define a map from \widehat{ECH}(M) to \widehat{HF}(-M). This map is defined by counting J-holomorphic curves in a symplectic cobordism but, unlike the definition of the map from \widehat{HF} and \widehat{ECH}, the construction is subtle and seems related to a Floer theoretic implementation of Poincaré duality in (S1)^{2g}.
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