In dimensions n at least 4, S^2 x S^(n-2) is not cancellable, so connected sum decomposition is not unique; for simply connected manifolds the same failure is claimed for n at least 17.
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Connected sum decompositions of high-dimensional manifolds
In dimensions n at least 4, S^2 x S^(n-2) is not cancellable, so connected sum decomposition is not unique; for simply connected manifolds the same failure is claimed for n at least 17.