Splicing integer framed knot complements and bordered heegaard floer homology

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We consider the following question: when is the manifold obtained by gluing together two knot complements an L-space? Hedden and Levine proved that splicing 0-framed complements of nontrivial knots never produces an L-space. We extend this result to allow for arbitrary integer framings. We find that splicing two integer framed nontrivial knot complements only produces an L-space if both knots are L-space knots and the framings lie in an appropriate range. The proof involves a careful analysis of the bordered Heegaard Floer invariants of each knot complement.

Original languageEnglish (US)
Pages (from-to)715-748
Number of pages34
JournalQuantum Topology
Issue number4
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Geometry and Topology


  • Bordered Floer homology
  • Knots
  • L-spaces
  • Toroidal manifolds


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