Links of rational singularities, L-spaces and LO fundamental groups

摘要

We prove that the link of a complex normal surface singularity is an L-space if and only if the singularity is rational. This via a result of Hanselman et al. (Taut foliations on graph manifolds, 2015. arXiv: 1508.0591), proving the conjecture of Boyer et al. (Math Ann 356(4): 1213-1245, 2013), shows that a singularity link is not rational if and only if its fundamental group is left-orderable if and only if it admits a coorientable taut foliation.