Splicing integer framed knot complements and bordered Heegaard Floer homology
Jonathan Hanselman
Princeton University, USA
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Abstract
We consider the following question: when is the manifold obtained by gluing together two knot complements an -space? Hedden and Levine proved that splicing 0-framed complements of nontrivial knots never produces an -space. We extend this result to allow for arbitrary integer framings. We find that splicing two integer framed nontrivial knot complements only produces an -space if both knots are -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.
Cite this article
Jonathan Hanselman, Splicing integer framed knot complements and bordered Heegaard Floer homology. Quantum Topol. 8 (2017), no. 4, pp. 715–748
DOI 10.4171/QT/100