Strong Heegaard diagrams and strong L–spaces

Joshua Evan Greene, Adam Simon Levine

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We study a class of 3–manifolds called strong L–spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that every strong L–space is the branched double cover of an alternating link in the three-sphere. For example, we establish this fact for a strong L–space admitting a strong Heegaard diagram of genus 2 via an explicit classification. We also show that there exist finitely many strong L–spaces with bounded order of first homology; for instance, through order eight, they are connected sums of lens spaces. The methods are topological and graph-theoretic. We discuss many related results and questions.

Original languageEnglish (US)
Pages (from-to)3167-3208
Number of pages42
JournalAlgebraic and Geometric Topology
Issue number6
StatePublished - Dec 15 2016

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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