奇维球面映射延拓问题的可判定性
Decidability of the extension problem for maps into odd-dimensional spheres
摘要：
在最近的一篇论文中，证明了定义在子空间$A \subseteq X$上的连续映射$A \to Y$的存在性问题是不可判定的，即使对$Y$是偶数维球面也是如此.在本文中，我们证明了同样的问题$Y$的奇数维球是可判定的。更一般地，这同样适用于其同伦群$π_k Y$对于$k>2d$是有限的任何$d$连接的目标空间$Y$。
英文摘要：
In a recent paper, it was shown that the problem of existence of a continuous map $X \to Y$ extending a given map $A \to Y$ defined on a subspace $A \subseteq X$ is undecidable, even for $Y$ an even-dimensional sphere. In the present paper, we prove that the same problem for $Y$ an odd-dimensional sphere is decidable. More generally, the same holds for any $d$-connected target space $Y$ whose homotopy groups $π_k Y$ are finite for $k>2d$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
