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2016 Strong Heegaard diagrams and strong L–spaces
Joshua Greene, Adam Levine
Algebr. Geom. Topol. 16(6): 3167-3208 (2016). DOI: 10.2140/agt.2016.16.3167


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.


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Joshua Greene. Adam Levine. "Strong Heegaard diagrams and strong L–spaces." Algebr. Geom. Topol. 16 (6) 3167 - 3208, 2016.


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

zbMATH: 1361.57019
MathSciNet: MR3584256
Digital Object Identifier: 10.2140/agt.2016.16.3167

Primary: 57M27 , 57R58

Keywords: $3$–manifolds , Heegaard diagrams , Heegaard Floer homology , L–spaces

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 6 • 2016
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