Strong Heegaard diagrams and strong L-spaces

Joshua Evan Greene; Adam Simon Levine

doi:10.2140/agt.2016.16.3167

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arXiv · 1411.6329

Strong Heegaard diagrams and strong L-spaces

Joshua Evan Greene·Adam Simon Levine

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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 two 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 Evan Greene, Adam Simon Levine. 2014-11-24. Strong Heegaard diagrams and strong L-spaces. https://doi.org/10.2140/agt.2016.16.3167

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