Non-separating spheres and twisted Heegaard Floer homology

Abstract

If a 3--manifold $Y$ contains a non-separating sphere, then some twisted Heegaard Floer homology of $Y$ is zero. This simple fact allows us to prove several results about Dehn surgery on knots in such manifolds. Similar results have been proved for knots in $L$--spaces.

15 pages, 1 figure

References in corpus (3)

• Knot Floer homology detects fibred knots
• Product Formulae for Ozsvath-Szabo 4-manifold Invariants
• The twisted Floer homology of torus bundles

Cited by in corpus (6)

• Khovanov module and the detection of unlinks
• Link Floer homology also detects split links
• Diagonals and A-infinity Tensor Products
• Dehn surgery and non-separating two-spheres
• Three-manifold mutations detected by Heegaard Floer homology
• Null-homotopic knots have Property R