Prime decomposition of 3-manifolds

In mathematics, the prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) finite collection of prime 3-manifolds. A manifold is prime if it is not homeomorphic to any connected sum of manifolds, except for the trivial connected sum of the manifold with a sphere of the same dimension, M ≅ M # S n {\textstyle M\cong M\#S^{n}} .

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