Abstract
A di-embedding of the $n$-cube $I^n$ into $\mathbb{r}^n$ is a map $I ^n\to \mathbb{R}^n$ 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 $I^1 \to \mathbb{R}$.
Citation
Praphat Fernandes. Andrew Nicas. "Classification of di-embeddings of the $n$-cube into $\mathbb {R}^n$." Homology Homotopy Appl. 9 (1) 213 - 220, 2007.
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