On Plumbed L-spaces

TL;DR

This paper investigates the properties of L-spaces arising from links of isolated complete intersection surface singularities, establishing conditions under which these spaces are rational or admit symplectic fillings.

Contribution

It proves that such L-spaces are links of rational singularities and characterizes non-L-spaces as those admitting symplectic fillings with positive second Betti number.

Findings

L-spaces from these links are links of rational singularities

Non-L-spaces admit symplectic fillings with b_2^+ > 0

All integral homology sphere L-spaces in this class are characterized

Abstract

L-spaces were introduced by Ozsvath and Szabo using the Heegaard Floer Homology. In the quest for L-spaces we consider links of isolated complete intersection surface singularities. We show that if such a manifold is an L-space, then it is a link of a rational singularity. We also prove that if it is not an L-space then it admits a symplectic filling with $b_2^+>0$. Based on these results we pin down all integral homology sphere L-spaces in this realm.