# prime n-manifold

A n-manifold (http://planetmath.org/TopologicalManifold) $M$ is called if for all the factorizations of $M$, as a connected sum (http://planetmath.org/ConnectedSum2) $M=M_{1}\#M_{2}$, one finds that one of the factors $M_{1}$ or $M_{2}$ is the n-sphere $S^{n}$.

The importance for 3-manifold is the existence and uniqueness prime decomposition theorem which says: Each 3-manifold can be decomposed as a connected sum of prime manifolds.

Title prime n-manifold PrimeNmanifold 2013-03-22 16:05:37 2013-03-22 16:05:37 juanman (12619) juanman (12619) 14 juanman (12619) Feature msc 57N10