Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 6 (2016), 3167-3208.
Strong Heegaard diagrams and strong L–spaces
We study a class of –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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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