# irreducible n-manifold

An $n$-manifold (http://planetmath.org/TopologicalManifold) $M$ is called irreducible if for each embedding of a standard $(n-1)$-sphere $S^{n-1}$ in $M$, there is an embedding of a standard $n$-ball (http://planetmath.org/StandardNBall) $D^{n}$ in $M$ such that the image of the boundary $\partial D^{n}$ coincides with the image of $S^{n-1}$.

In case of dimension three it can be proved that each irreducible 3-manifold is also a prime (http://planetmath.org/Prime3Manifold) 3-manifold.

Title irreducible n-manifold IrreducibleNmanifold 2013-03-22 16:05:43 2013-03-22 16:05:43 juanman (12619) juanman (12619) 12 juanman (12619) Definition msc 57N10