Splicing integer framed knot complements and bordered Heegaard Floer homology

Jonathan Hanselman

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arXiv · 1409.1912

Splicing integer framed knot complements and bordered Heegaard Floer homology

Jonathan Hanselman

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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.

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BibTeX RIS

Jonathan Hanselman. 2014-09-05. Splicing integer framed knot complements and bordered Heegaard Floer homology. https://arxiv.org/abs/1409.1912

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