Mathematics Colloquia and Seminars

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Rank vs. Genus


Speaker: Tao Li, Boston College
Location: 2112 MSB
Start time: Tue, Jun 5 2012, 3:10PM

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.