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Small 3-Manifolds of Large Genus


We prove the existence of pure braids with arbitrarily many strands which are small, i.e. the complements contain no closed incompressible surface which is not boundary parallel. This implies the existence of irreducible non-Haken 3-manifolds of arbitrarily high Heegaard genus.

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Agol, I. Small 3-Manifolds of Large Genus. Geometriae Dedicata 102, 53–64 (2003).

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  • Haken
  • Heegaard genus
  • 3-manifold