3-manifold - Important Conjectures

Important Conjectures

Some of these are thought to be solved, as of March 2007. Please see specific articles for more information.

  • PoincarĂ© conjecture — see also Solution of the PoincarĂ© conjecture
  • Thurston's geometrization conjecture
  • Virtually fibered conjecture
  • Virtually Haken conjecture
  • Cabling conjecture
  • Surface subgroup conjecture
  • Simple loop conjecture
  • The smallest hyperbolic 3-manifold is the Weeks manifold.
  • Lubotzy-Sarnak conjecture on property tau

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