Let $f:D \to D$ homeomorphism of $k$ codimension manifold (closed, compact, without boundary) to itself. ($D \subset \mathbb{R}^{n+k}$). For which $f$ does homeorophism $g: \mathbb{R}^{n+k} \to \mathbb{R}^{n+k}$ (homeomorphism $\mathbb{R}^{n+k}$ to itself) that's $g|_D=f$ exist? Does some classification of homeomorphism's having that property exist?
I found that, but its only for k=2. http://arxiv.org/abs/0910.4949v2
