Rational Homotopy Type and Computability

Given a simplicial pair (X, A), complex Y, and map $$f:A \rightarrow Y$$ , does f have an extension to X? We show that for fixed this question is algorithmically decidable all X, A, if Y has the rational homotopy type of H-space. As corollary, many questions related bundle structures over finite are likely decidable. Conversely, other at least as hard certain special cases Hilbert’s tenth problem which known or suspected be undecidable.