The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y , equipped with a Spin c structure. Given a Heegaard splitting of Y = U 0 U 1 , these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of relative to certain totally real subspaces associated to U 0 and U 1 .
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Ozsváth et al. (2004) studied this question.
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