Mathematical Research Letters
Volume 19 (2012)
Strong L-spaces and left-orderability
Pages: 1237 – 1244
We introduce the notion of a strong L-space, a closed, oriented three-manifold admitting a Heegaard diagram whose associated Heegaard Floer complex has rank equal to the order of the first homology of the manifold. Examples of strong L-spaces include the branched double covers of alternating links in the three-sphere. We prove that the fundamental group of a strong L-space is not left-orderable.