Surface subgroup conjecture
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In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that every compact, irreducible 3-manifold with infinite fundamental group has a non-peripheral surface subgroup. By "surface subgroup" we mean the fundamental group of a closed surface not the 2-sphere.
The conjecture is currently only open for closed 3-manifolds. Assuming the geometrization conjecture, the only open case is that of closed hyperbolic 3-manifolds.
[edit] See also
- Virtually Haken conjecture
- Ehrenpreiss conjecture
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