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On the Exactness of the Eckmann-Hilton Homotopy Sequence

Published online by Cambridge University Press:  20 November 2018

A. R. Pears
A. R. Pears*
Affiliation:
Queen Elizabeth College, University of London
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The theorem that the homotopy sequence is exact splits into six statements. Scherk ([4]) obviates the use of homotopy extension in the proof of one of these statements. The purpose of this note is to show that the method can be adapted to give a direct proof of the corresponding statement in the theorem that the Eckmann-Hilton homotopy sequence ([l]) is exact. The note is based on Eckmann' s exposition ([2]). We are concerned with the proof of b2, pp. 34–35.

Type
Notes and Problems
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 5 , December 1966 , pp. 671 - 673
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Eckmann, B. and Hilton, P. J., Groupes df homotopie et dualité. C. R. Acad. Sci. Paris 246 (1958) 2444–2446, 2555-2558.Google Scholar
2. Eckmann, B., Homotopie et Cohomologie. Séminaire de Mathématiques Supérieures - Eté 1964. Les Presses de I'Université de Montréal.Google Scholar
3. Hilton, P. J., An Introduction to Homotopy Theory. Cambridge Tracts in Mathematics No. 43. Cambridge University Press.Google Scholar
4. Scherk, P., On the exactness of the homotopy sequence. Canad. Math. Bull. 7 (1964), 617-618.Google Scholar