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
Canonical name	IrreducibleNmanifold
Date of creation	2013-03-22 16:05:43
Last modified on	2013-03-22 16:05:43
Owner	juanman (12619)
Last modified by	juanman (12619)
Numerical id	12
Author	juanman (12619)
Entry type	Definition
Classification	msc 57N10