The decomposition of 3-manifolds with several boundary components.

Incompressible surfaces in the exterior of a closed 3-braid

“…Then M x = A x S 1^. "^ (S 1 x D 2 ) it where A denotes an annulus and A the disc sum (see [4] or [5]), Fig. 2-8.…”

A unique decomposition theorem for 3-manifolds with connected boundary

“…Extension of results. The author uses the methods of this paper to show in [1] that there is a unique decomposition theorem for compact, orientable 3-manifolds with several boundary components. It is also shown in [1] that the problem of classifying the compact, orientable 3-manifolds with several boundary components reduces to the problem of classifying the A-prime 3-manifolds.…”