Computing all maps into a sphere

  title={Computing all maps into a sphere},
  author={Martin Cadek and Marek Krc{\'a}l and Jir{\'i} Matousek and Francis Sergeraert and Luk{\'a}s Vokr{\'i}nek and Uli Wagner},
Given topological spaces <i>X</i>,<i>Y</i>, a fundamental problem of algebraic topology is understanding the structure of all continuous maps <i>X</i> → <i>Y</i>. We consider a computational version, where <i>X</i>,<i>Y</i> are given as finite simplicial complexes, and the goal is to compute [<i>X</i>,<i>Y</i>], that is, all homotopy classes of such maps. We solve this problem in the <i>stable range</i>, where for some <i>d</i> ≥ 2, we have dim <i>X</i> ≤ 2<i>d</i>−2 and <i>Y</i> is (<i>d</i>-1… CONTINUE READING
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