Rank and genus of 3-manifolds

Details Rank and genus of 3-manifolds Rank and genus of 3-manifolds

2011-06-30

arxiv.org/abs/1106.6302v1

Mathematics

Geometric Topology

60 pages, 15 figures

Scientific paper

We construct a counterexample to the Rank versus Genus Conjecture, i.e. a
closed orientable hyperbolic 3-manifold with rank of its fundamental group
smaller than its Heegaard genus. Moreover, we show that the discrepancy between
rank and Heegaard genus can be arbitrarily large for hyperbolic 3-manifolds. We
also construct toroidal such examples containing hyperbolic JSJ pieces.

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