Are there some known results which give a classification of closed prime 3-manifolds up to their Heegaard diagrams? (That is, providing a collection of Heegaard diagrams which exhausts all prime manifolds.)
Thanks.
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1$\begingroup$ There's a recent paper on this topic: arxiv.org/abs/1509.05945 $\endgroup$– Ian AgolCommented Sep 27, 2015 at 0:54
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