Rational homotopy type and computability

07/21/2020

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by   Fedor Manin, et al.

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Given a simplicial pair (X,A), a simplicial complex Y, and a map f:A → 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 and only 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 decidable.