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| Paper IPM / M / 16144 |
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| Abstract: | |
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Let K denote a knot inside the homology sphere Y. The zero-framed longitude of K gives the complement of K in Y the structure of a bordered three-manifold, which may be denoted by Y(K). We compute the quasi-isomorphism 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 S3 it does not contain any incompressible tori. Consequently, if Y is an irreducible homology sphere L-space then Y is either S3, or the Poicaré sphere Σ(2,3,5), or it is hyperbolic.
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