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Paper   IPM / M / 16144
School of Mathematics
  Title:   Bordered Floer homology and existence of incompressible tori in homology spheres
  Author(s):  Eaman Eftekhary
  Status:   Published
  Journal: Compos. Math.
  Vol.:  154
  Year:  2018
  Pages:   1222-1268
  Supported by:  IPM
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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