The geometrization conjecture (now theorem) says that each $3$ dimensional manifold decomposes into canonical pieces which admit geometric structures. So, in general, a $3$ dimensional manifold does not admit a geometric structure. Furthermore I suppose that almost all $3$-manifolds do not admit a geometric structure. But I'm just looking for an example of such a $3$ manifold, since all examples I know admit geometric structures. Thank you very much!
2026-03-31 15:12:39.1774969959
Which $3$-manifolds do not admit a geometric structure?
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