Splicing knot complements and bordered Floer homology

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.

25 pages. Revised version, to appear in Crelle's Journal. Errors from the original version have been corrected

References in corpus (5)

• Ricci flow with surgery on three-manifolds
• Floer homology and knot complements
• Knot Floer homology detects fibred knots
• Bordered Heegaard Floer homology and the tau-invariant of cable knots
• On Plumbed L-spaces

Cited by in corpus (13)

• Bordered Floer homology and existence of incompressible tori in homology spheres
• Seifert vs slice genera of knots in twist families and a characterization of braid axes
• The signature of a splice
• A calculus for bordered Floer homology
• Instanton L-spaces and splicing
• Rank inequalities for the Heegaard Floer homology of branched covers
• Character varieties of knot complements and branched double-covers via the cord ring
• Cable knots are not thin
• A mnemonic for the Lipshitz-Ozsváth-Thurston correspondence
• Correction to the article: Floer homology and splicing knot complements
• Taut foliations, braid positivity, and unknot detection
• A Floer homology invariant for $3$-orbifolds via bordered Floer theory
• Cosmetic surgery in L-spaces and nugatory crossings