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arXiv · 2007.10632

Rational homotopy type and computability

Fedor Manin
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Abstract

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.

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Fedor Manin. 2020-07-21. Rational homotopy type and computability. https://doi.org/10.1007/s10208-022-09582-8

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