---
res:
  bibo_abstract:
  - '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 suchmaps.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
    tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and
    simplicial sets) with algorithmic tools from effective algebraic topology (locally
    effective simplicial sets and objects with effective homology). In contrast, [X,Y]
    is known to be uncomputable for general X,Y, since for X = S1 it includes a well
    known undecidable problem: testing triviality of the fundamental group of Y. In
    follow-up papers, the algorithm is shown to run in polynomial time for d fixed,
    and extended to other problems, such as the extension problem, where we are given
    a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or
    computing the Z2-index-everything in the stable range. Outside the stable range,
    the extension problem is undecidable.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Čadek, Martin
      foaf_surname: Čadek
  - foaf_Person:
      foaf_givenName: Marek
      foaf_name: Krcál, Marek
      foaf_surname: Krcál
      foaf_workInfoHomepage: http://www.librecat.org/personId=33E21118-F248-11E8-B48F-1D18A9856A87
  - foaf_Person:
      foaf_givenName: Jiří
      foaf_name: Matoušek, Jiří
      foaf_surname: Matoušek
  - foaf_Person:
      foaf_givenName: Francis
      foaf_name: Sergeraert, Francis
      foaf_surname: Sergeraert
  - foaf_Person:
      foaf_givenName: Lukáš
      foaf_name: Vokřínek, Lukáš
      foaf_surname: Vokřínek
  - foaf_Person:
      foaf_givenName: Uli
      foaf_name: Wagner, Uli
      foaf_surname: Wagner
      foaf_workInfoHomepage: http://www.librecat.org/personId=36690CA2-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-1494-0568
  bibo_doi: 10.1145/2597629
  bibo_issue: '3'
  bibo_volume: 61
  dct_date: 2014^xs_gYear
  dct_identifier:
  - UT:000337201400003
  dct_language: eng
  dct_publisher: ACM@
  dct_title: Computing all maps into a sphere@
...