Abstract
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 language | English (US) |
---|---|
Pages (from-to) | 715-748 |
Number of pages | 34 |
Journal | Quantum Topology |
Volume | 8 |
Issue number | 4 |
DOIs | |
State | Published - 2017 |
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Geometry and Topology
Keywords
- Bordered Floer homology
- Knots
- L-spaces
- Toroidal manifolds