[DevelopingElk]

Manifolds are generally considered objects of themselves, and it may be difficult to embed then in higher dimensional objects. This is especially the case for tricky manifolds like those with a Kervaire invariant of 1.

[red_trumpet]

At this point it might be worthy to note the Whitney Embedding Theorem[1], which states:

> Every smooth n-dimensional manifold can be embedded into R^{2n}.

[1] https://en.wikipedia.org/wiki/Whitney_embedding_theorem