We prove that a C∞ semialgebraic local diffeomorphism of ℝⁿ with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if n − 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of ℝⁿ. Our conjecture implies a very known conjecture of Z. Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature.

中文翻译：

---

线性算子的满射性和半代数全局微分同胚

我们证明，如果n − 1个合适的线性偏微分算子是满射的，则具有余维数大于或等于 2 的非属性集的 ℝ ⁿ的C ∞半代数局部微分同胚是全局微分同胚。^{然后我们对 ℝ n}的多项式局部微分同胚提出一个新的解析猜想。我们的猜想暗示了Z的一个众所周知的猜想。耶洛内克。我们进一步将这些算子的满射性与纤维化概念联系起来，并提出了半代数映射的一般全局单射性定理，该定理最终统一并概括了先前的文献结果。