Computing all maps into a sphere

Details Computing all maps into a sphere Computing all maps into a sphere

2011-05-31

arxiv.org/abs/1105.6257v3

Computer Science

Computational Geometry

42 pages; only minor updates and corrections compared to the previous version

Scientific paper

We present an algorithm for computing [X,Y], i.e., all homotopy classes of continuous maps X -> Y, where X,Y are topological spaces given as finite simplicial complexes, Y is (d-1)-connected for some d>1 (for example, Y can be the d-dimensional sphere), and dim X<=2d-2. These conditions on X,Y guarantee that [X,Y] has a natural structure of a finitely generated Abelian group, and the algorithm finds its structure.

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