Floer Simple Manifolds and L-Space Intervals

Abstract

An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-space filling, or an interval of L-space fillings. In the latter case, which we call "Floer simple," we construct an invariant which computes the interval of L-space filling slopes from the Turaev torsion and a given slope from the interval's interior. As applications, we give a new proof of the classification of Seifert fibered L-spaces over $S^2$, and prove a special case of a conjecture of Boyer and Clay about L-spaces formed by gluing three-manifolds along a torus.

50 pages, 2 figures

References in corpus (8)

• Floer homology and knot complements
• Knot Floer homology detects fibred knots
• Lens space surgeries and L-space homology spheres
• Approximating $C^0$-foliations by contact structures
• $C^0$ Approximations of foliations
• Berge-Gabai knots and L-space satellite operations
• A calculus for bordered Floer homology
• Splicing integer framed knot complements and bordered Heegaard Floer homology

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