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Boundary parallel

From Wikipedia, the free encyclopedia

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.[1]

An example

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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.)

Context and applications

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Further reading

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See also

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References

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  1. ^ Definition 3.4.7 in Schultens, Jennifer (2014). Introduction to 3-manifolds. Graduate studies in mathematics. Vol. 151. AMS. ISBN 978-1-4704-1020-9.