Strong Heegaard diagrams and strong L–spaces

Greene, Joshua¹ ; Levine, Adam²

¹Department of Mathematics, Boston College, Maloney Hall, Fifth Floor, Chestnut Hill, MA 02467, United States
²Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, United States

Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3167-3208

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.3167

Classification : 57M27, 57R58
Keywords: $3$–manifolds, Heegaard diagrams, Heegaard Floer homology, L–spaces

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