Laminar free hyperbolic 3-manifolds

• Autores: Sergio R. Fenley
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 82, Nº 2, 2007, págs. 247-321
• Idioma: inglés
• DOI: 10.4171/cmh/92
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• Resumen

  • The purpose of the article is to prove that there are infinitely many closed hyperbolic 3-manifolds which do not admit essential laminations. The manifolds are obtained by Dehn surgery on torus bundles over the circle. This gives a definitive negative answer to a fundamental question posed by Gabai and Oertel when they introduced essential laminations. The proof is obtained by analysing group actions on on trees and showing that certain 3-manifold groups only have trivial actions on trees. There are corollaries concerning the existence of Reebless foliations and pseudo-Anosov flows.