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.