In mathematics, a closed n-manifold N embedded in an (n + 1)-manifold M is boundary parallel (or ∂-parallel, or peripheral) if there is an isotopy of N onto a boundary component of M. Consider the annulus
Let π denote the projection map 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.)