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Paper IPM / M / 16144  


Abstract:  
Let K denote a knot inside the homology sphere Y. The zeroframed longitude of K gives the complement of K in Y the structure of a bordered threemanifold, which may be denoted by Y(K). We compute the quasiisomorphism type of the bordered Floer complex of Y(K) in terms of the knot Floer complex associated with K. As a corollary, we show that if a homology sphere has the same Heegaard Floer homology as S^{3} it does not contain any incompressible tori. Consequently, if Y is an irreducible homology sphere Lspace then Y is either S^{3}, or the PoicarÃ© sphere Σ(2,3,5), or it is hyperbolic.
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