L-spaces, taut foliations, and graph manifolds. (23rd March 2020) - Hanselman, Jonathan; Rasmussen, Jacob; Rasmussen, Sarah Dean; Watson, Liam
Abstract : 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 $\unicode[STIX]{x1D70B}_{1}(Y)$ is not left-orderable.