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

2015/10/24 by Némethi, András
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1510.07128

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.

Related

• On Plumbed L-spaces
• Fundamental groups of links of isolated singularities
• Topology, geometry, and equations of normal surface singularities
• Links and analytic invariants of superisolated singularities
• Links of complex analytic singularities