Are two given maps homotopic? An algorithmic viewpoint - Filakovský, Marek; Vokřínek, Lukas; Algorithms for Embeddings and Homotopy Theory (Foundations of Computational Mathematics, 2020)
This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps 𝑓,𝑔:𝑋→𝑌, and the second computes the group [𝛴𝑋,𝑌]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to 𝐴⊆𝑋.
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