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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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Sufficient Conditions for Free Indecomposability
An interesting fact was relayed to me in another question of mine that
If $M$ is any closed manifold with universal cover homeomorphic to $R^n$ for $n>1$ then $\pi_1(M)$ is freely indecomposable. …
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Fundamental groups of closed hyperbolic 3-manifolds are freely indecomposable
I believe the following statement is true, and I've even seen it referenced here. Could someone point me to a proof?
The fundamental group of a closed hyperbolic 3-manifold is not a free product.
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