Algebraic & Geometric Topology

Strong Heegaard diagrams and strong L–spaces

Joshua Greene and Adam Levine

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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.

Article information

Algebr. Geom. Topol., Volume 16, Number 6 (2016), 3167-3208.

Received: 9 December 2014
Accepted: 2 June 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology

$3$–manifolds Heegaard diagrams Heegaard Floer homology L–spaces


Greene, Joshua; Levine, Adam. Strong Heegaard diagrams and strong L–spaces. Algebr. Geom. Topol. 16 (2016), no. 6, 3167--3208. doi:10.2140/agt.2016.16.3167.

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