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

Abstract

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 recent result of Hanselman, J. Rasmussen, S. D. Rasmussen and Watson (proving the conjecture of Boyer, Gordon and Watson), 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.