Solid-torus recognition by a compression disk
= Solid-torus recognition by a compression disk
A compact orientable <irreducible three-manifold> with connected torus boundary which is compressible is a <solid torus>. Compressing along a <compression disk> gives an embedded sphere. The compressed component has one sphere boundary and irreducibility makes it a ball; undoing compression attaches one one-handle, giving $D^2\times S^1$.