L-space fillings and generalized solid tori

Much work has been done recently towards trying to understand the topological significance of being an L-space. Building on work of Rasmussen and Rasmussen, we give a topological characterisation of Floer simple manifolds such that all non-longitudinal fillings are L-spaces. We use this to partially classify L-space twisted torus knots in $S^1\times S^2$ and resolve a question asked by Rasmussen and Rasmussen.