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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Homotopy groups of suspended classifying spaces: An experimental approach


Authors: Ana Romero and Julio Rubio
Journal: Math. Comp. 82 (2013), 2237-2244
MSC (2010): Primary 68W05, 55-04, 55Q99
Published electronically: February 28, 2013
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Abstract: 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.


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Additional Information

Ana Romero
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, C/ Luis de Ulloa s/n, 26004 Logroño, Spain
Email: ana.romero@unirioja.es

Julio Rubio
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, C/ Luis de Ulloa s/n, 26004 Logroño, Spain
Email: julio.rubio@unirioja.es

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02680-4
PII: S 0025-5718(2013)02680-4
Received by editor(s): October 7, 2011
Received by editor(s) in revised form: January 11, 2012
Published electronically: February 28, 2013
Additional Notes: Both authors were partially supported by Ministerio de Ciencia e Innovación, Spain, project MTM2009-13842-C02-01
Article copyright: © Copyright 2013 American Mathematical Society