# Computing All Maps into a Sphere

@article{adek2014ComputingAM, title={Computing All Maps into a Sphere}, author={Martin {\vC}adek and Marek Krc{\'a}l and Jir{\'i} Matousek and Francis Sergeraert and Luk{\'a}s Vokr{\'i}nek and Uli Wagner}, journal={Journal of the ACM (JACM)}, year={2014}, volume={61}, pages={1 - 44} }

Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X → Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of such maps. We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d−2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical…

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