Mathematical Research Letters

Volume 19 (2012)

Number 6

Strong L-spaces and left-orderability

Pages: 1237 – 1244



Adam Simon Levine (Department of Mathematics, Brandeis University, Waltham, Massachusetts, U.S.A.)

Sam Lewallen (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)


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.

Published 18 July 2013