Strong Heegaard diagrams and strong L–spaces

Greene, Joshua; Levine, Adam

doi:10.2140/agt.2016.16.3167

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Strong Heegaard diagrams and strong L–spaces

Joshua Evan Greene and Adam Simon Levine

Algebraic & Geometric Topology 16 (2016) 3167–3208

DOI: 10.2140/agt.2016.16.3167

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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 57M27, 57R58

References

Publication

Received: 9 December 2014

Accepted: 2 June 2016

Published: 15 December 2016

Authors

Joshua Evan Greene
Department of Mathematics Boston College Maloney Hall, Fifth Floor Chestnut Hill, MA 02467 United States
http://www2.bc.edu/joshua-e-greene
Adam Simon Levine
Department of Mathematics Princeton University Fine Hall Washington Road Princeton, NJ 08544 United States
http://www.math.princeton.edu/~asl2

Volume 16, issue 6 (2016)