## Algebraic & Geometric Topology

### Strong Heegaard diagrams and strong L–spaces

#### Abstract

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

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

Dates
Accepted: 2 June 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841257

Digital Object Identifier
doi:10.2140/agt.2016.16.3167

Mathematical Reviews number (MathSciNet)
MR3584256

Zentralblatt MATH identifier
1361.57019

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1510841257

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