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 Lspace 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 [6] about L-spaces formed by gluing three-manifolds along a torus.

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If Y is a closed orientable graph manifold, we show that Y admits a coorientable taut foliation if and only if Y is not an L-space. Combined with previous work of Boyer and Clay, this implies that Y is an L-space if and only if π1(Y ) is not left-orderable.