A case study of A8-structure

  1. Alcaraz, A.B. 1
  2. Rubio, J. 2
  3. Sergeraert, F. 3
  1. 1 Universidad del País Vasco/Euskal Herriko Unibertsitatea
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    Universidad del País Vasco/Euskal Herriko Unibertsitatea

    Lejona, España

    ROR https://ror.org/000xsnr85

  2. 2 Universidad de La Rioja
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    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  3. 3 Institut Fourier
    info

    Institut Fourier

    Saint-Martin-d’Hères, Francia

    ROR https://ror.org/05rwrfh97

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Revista:
Georgian Mathematical Journal

ISSN: 1072-947X

Año de publicación: 2010

Volumen: 17

Número: 1

Páginas: 57-77

Tipo: Artículo

DOI: 10.1515/GMJ.2010.003 SCOPUS: 2-s2.0-79952488678 WoS: WOS:000277062900004 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Georgian Mathematical Journal

Resumen

The computer program Kenzo is used to study complex A∞-structures coming from iterated loop spaces. The methods of constructive algebraic topology, due to the authors, do produce chain complexes of finite type and chain equivalences with the Hopf algebras canonically associated to the loop spaces. These chain complexes of finite type are therefore endowed with A∞-structures. It is then experimentally observed, using the Kenzo program, that A∞-structures of arbitrarily high orders are nontrivial in these objects. This case study is a good illustration of the computing tools given to the topologists by the Kenzo program.