The image of the branch set of a piecewise linear (PL)‐branched cover between PL $n$‐manifolds is a simplicial $(n-2)$‐complex. We demonstrate that the reverse implication also holds: an open and discrete map $f:{\mathbb{S}}^n\to {\mathbb{S}}^n$ with the image of the branch set contained in a simplicial $(n-2)$‐complex is equivalent up to homeomorphism to a PL‐branched cover.

中文翻译：

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具有分段线性分支集图像的开放图和离散图是分段线性图

PL之间的分段线性（PL）分支的封面的分支集的图像 $ñ$歧管是简单的 $（ñ-\mathrm{2个}）$-复杂的。我们证明反向蕴涵也成立：一个开放且离散的地图$F：{\mathbb{小号}}^{ñ}\to {\mathbb{小号}}^{ñ}$ 与包含在一个简单的分支集的图像 $（ñ-\mathrm{2个}）$复杂度与PL分支封面的同胚等效。