论文标题
合理同型类型和可计算性
Rational homotopy type and computability
论文作者
论文摘要
给定简单对$（x，a）$，一个简单的复杂$ y $和地图$ f：a \ y $，$ f $是否扩展到$ x $？我们表明，对于固定的$ y $，如果$ y $具有H-Space的合理同型类型，则此问题在所有$ x $，$ a $和$ f $上都是算法决定的。作为推论，许多与有限复合体上捆绑结构有关的问题可能是可以决定的。相反，对于所有其他$ y $，这个问题至少与某些希尔伯特（Hilbert）第十个问题的特殊案例一样困难，这些问题已知或怀疑是不可决定的。
Given a simplicial pair $(X,A)$, a simplicial complex $Y$, and a map $f:A \to Y$, does $f$ have an extension to $X$? We show that for a fixed $Y$, this question is algorithmically decidable for all $X$, $A$, and $f$ if $Y$ has the rational homotopy type of an H-space. As a corollary, many questions related to bundle structures over a finite complex are likely decidable. Conversely, for all other $Y$, the question is at least as hard as certain special cases of Hilbert's tenth problem which are known or suspected to be undecidable.
