Surface subgroup conjecture

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In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3-manifold with infinite fundamental group has a surface subgroup. By "surface subgroup" we mean the fundamental group of a closed surface not the 2-sphere. This problem is listed as Problem 3.75 in Rob Kirby's problem list.

Assuming the geometrization conjecture, the only open case is that of closed hyperbolic 3-manifolds.

[edit] See also

• Virtually Haken conjecture
• Ehrenpreiss conjecture