Decidability of the extension problem for maps into odd-dimensional spheres

Abstract

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 ${\pi }_{k}Y$ are finite for $k>2d$.

6 pages

References in corpus (2)

• Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension
• Extendability of continuous maps is undecidable