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 $I\backslash times\; S^1$. Let π denote the projection map

$\backslash pi:I\backslash times\; S^1\backslash rightarrow\; S^1,\backslash qquad(x,z)\backslash mapsto\; z.$

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.)

Annulus.circle.bijective-projection.pngAnnulus.circle.nulhomotopic.png

Geometric topology