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arXiv · 1210.7055

Splicing knot complements and bordered Floer homology

Matthew Hedden·Adam Simon Levine
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Abstract

We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology rank strictly greater than one. In particular, splicing the complements of nontrivial knots in the 3-sphere never produces an L-space. The proof uses bordered Floer homology.

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Matthew Hedden, Adam Simon Levine. 2015-09-10. Splicing knot complements and bordered Floer homology. https://doi.org/10.1515/crelle-2014-0064

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