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arXiv:1210.7055 [math.GT]AbstractReferencesReviewsResources

Splicing knot complements and bordered Floer homology

Matthew Hedden, Adam Simon Levine

Published 2012-10-26, updated 2015-09-10Version 2

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.

Comments: 25 pages. Revised version, to appear in Crelle's Journal. Errors from the original version have been corrected
Categories: math.GT, math.SG
Subjects: 57M27, 57R58
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