Connected Sum Decomposition
Every compact 3-manifold is the connected sum of a unique collection of prime 3-manifolds.
See also
Jaco-Shalen-Johannson Torus DecompositionExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Connected Sum Decomposition." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConnectedSumDecomposition.html