L-spaces, taut foliations, and graph manifolds
Jonathan Hanselman, Jacob Rasmussen, Sarah Dean Rasmussen, Liam Watson
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.
Topics & Concepts
MathematicsGraphCombinatoricsPure mathematicsFoliation (geology)Manifold (fluid mechanics)Discrete mathematicsDifferential geometryDual graphImmersion (mathematics)Geometric and Algebraic TopologyHomotopy and Cohomology in Algebraic TopologyAdvanced Topology and Set Theory