Floer simple manifolds and L-space intervals

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An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-space filling, or an interval of L-space fillings. In the latter case, which we call “Floer simple,” we construct an invariant which computes the interval of L-space filling slopes from the Turaev torsion and a given slope from the interval's interior. As applications, we give a new proof of the classification of Seifert fibered L-spaces over S2, and prove a special case of a conjecture of Boyer and Clay [6] about L-spaces formed by gluing three-manifolds along a torus.

Original languageEnglish (US)
Pages (from-to)738-805
Number of pages68
JournalAdvances in Mathematics
StatePublished - Dec 15 2017
Externally publishedYes


  • Heegaard Floer homology
  • L-space

ASJC Scopus subject areas

  • Mathematics(all)


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