Boundary parallel

In mathematics, a closed "n"-manifold embedded in an ("n" + 1)-manifold is boundary parallel (or ∂-parallel, or peripheral) if it can be isotoped onto a boundary component.

An example

Consider the annulus $I\; imes\; S^1$. Let π denote the projection
$pi:I\; imes\; S^1\; ightarrow\; S^1,qquad(x,z)mapsto\; z.$

If a circle "S" is embedded into the annulus so that π restricted to "S" is a bijection, then "S" is boundary parallel. (The converse is not true.)

If, on the other hand, a circle "S" is embedded into the annulus so that π restricted to "S" is not surjective, then "S" is not boundary parallel. (Again, the converse is not true.)