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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Classification of exterior and proper fibrations
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by J. M. García-Calcines, P. R. García-Díaz and A. Murillo PDF
Proc. Amer. Math. Soc. 148 (2020), 3175-3185 Request permission

Abstract:

As in the classical setting, we classify a large class of exterior fibrations in the based exterior homotopy category. More precisely, the fibration sequences $F\to E\to X$ of path-connected based exterior CW-complexes are in bijective correspondence with the based exterior homotopy classes of maps from $X$ to a universal exterior CW-complex $Y_F$. As a result we classify proper fibrations between CW-complexes.
References
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Additional Information
  • J. M. García-Calcines
  • Affiliation: Departamento de Matemáticas, Estadística e I.O., Universidad de La Laguna, Ap. 456, 38200 La Laguna, Spain
  • Email: jmgarcal@ull.es
  • P. R. García-Díaz
  • Affiliation: Departamento de Matemáticas, Estadística e I.O., Universidad de La Laguna, Ap. 456, 38200 La Laguna, Spain
  • Email: pedroruyman@gmail.com
  • A. Murillo
  • Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Ap. 59, 29080 Málaga, Spain
  • MR Author ID: 294447
  • ORCID: 0000-0002-2681-274X
  • Email: aniceto@uma.es
  • Received by editor(s): June 3, 2019
  • Received by editor(s) in revised form: November 13, 2019
  • Published electronically: February 26, 2020
  • Additional Notes: This work has been supported by the MICINN grant MTM2016-78647 of the Spanish Government and by the Junta de Andalucía grant FQM-213

  • Dedicated: To Fernando Murillo, in memoriam.
  • Communicated by: Mark Behrens
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 3175-3185
  • MSC (2010): Primary 55P57, 55R05, 55R15
  • DOI: https://doi.org/10.1090/proc/14956
  • MathSciNet review: 4099802