Surface subgroup conjecture
- Surface subgroup conjecture
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.
ee also
*Virtually Haken conjecture
*Ehrenpreiss conjecture
References
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