Homotopy groups of suspended classifying spaces: An experimental approach

  1. Romero, A. 1
  2. Rubio, J. 1
  1. 1 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Mathematics of Computation

ISSN: 0025-5718

Year of publication: 2013

Volume: 82

Issue: 284

Pages: 2237-2244

Type: Article

Export: RIS
DOI: 10.1090/S0025-5718-2013-02692-0 SCOPUS: 2-s2.0-84880687728 WoS: 000326291500014 lock_openOpen access editor
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When the results of a computer program are compared to some theorems proved on a theoretical basis three situations can occur: there can be an agreement between both approaches, the computer program can obtain calculations not covered by the theorems, or a discrepancy can be found between both methods. In this paper we report on a work where the three above mentioned situations happen. We have enhanced the Computer Algebra called Kenzo to deal with the computation of homotopy groups of suspended classifying spaces, a problem tackled by Mikhailov and Wu in a paper published in the journal Algebraic and Geometric Topology. Our experimental approach, based on completely different methods from those by Mikhailov and Wu, has allowed us in particular to detect an error in one of their published theorems. © 2013 American Mathematical Society.