Abstract
We present an algorithm for computing [X,Y], i.e., all homotopy classes of continuous maps X -} Y , where X and 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-1. These conditions on X and Y guarantee that [X,Y] has a natural structure of a fi nitely generated Abelian group, and the algorithm finds generators and relations for it.
We combine several tools and ideas from homotopy theory (such as Postnikov systems, simplicial sets, and obstruction theory) with algorithmic tools from effective algebraic topology (objects with effective homology).