Classification of di-embeddings of the n-cube into Rⁿ

Praphat Fernandes and Andrew Nicas

A di-embedding of the n-cube Iⁿ into Rⁿ is a map Iⁿ → Rⁿ which is a dihomeomorphism onto its image. We show that such a map is, up to a permutation of coordinates, an n-fold product of 1-dimensional orientation preserving embeddings I¹ → R.

Homology, Homotopy and Applications, Vol. 9 (2007), No. 1, pp.213-220.

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