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Classification of exterior and proper fibrations


Authors: J. M. García-Calcines, P. R. García-Díaz and A. Murillo
Journal: Proc. Amer. Math. Soc. 148 (2020), 3175-3185
MSC (2010): Primary 55P57, 55R05, 55R15
DOI: https://doi.org/10.1090/proc/14956
Published electronically: February 26, 2020
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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.


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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
Email: aniceto@uma.es

DOI: https://doi.org/10.1090/proc/14956
Keywords: Proper homotopy theory, exterior homotopy theory, exterior fibration, proper fibration, Brown representability.
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
Article copyright: © Copyright 2020 American Mathematical Society