Lifting Gottlieb sets and duality

Yoon, Yeon Soo

doi:10.1090/S0002-9939-1993-1184089-7

Lifting Gottlieb sets and duality
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Proc. Amer. Math. Soc. 119 (1993), 1315-1321 Request permission

Abstract:

Let $p:{E_f} \to X$ be a fibration induced by a map $f:X \to Y$ from the path space fibration $\varepsilon :PY \to Y$. Let $g:A \to X$ be cyclic. When does $g$ lift to a map $A \to {E_f}$ which is cyclic? We give an answer of this question for arbitrary $A$ and $Y$. Also, we give an answer in the dual situation.

References

Daniel Henry Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729–756. MR 275424, DOI 10.2307/2373349
I. G. Halbhavi and K. Varadarajan, Gottlieb sets and duality in homotopy theory, Canadian J. Math. 27 (1975), no. 5, 1042–1055. MR 391085, DOI 10.4153/CJM-1975-110-0

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spaces

C. S. Hoo, Lifting Gottlieb sets, J. London Math. Soc. (2) 14 (1976), no. 3, 535–544. MR 438339, DOI 10.1112/jlms/s2-14.3.535
K. L. Lim, On cyclic maps, J. Austral. Math. Soc. Ser. A 32 (1982), no. 3, 349–357. MR 652412
Robert M. Switzer, Algebraic topology—homotopy and homology, Die Grundlehren der mathematischen Wissenschaften, Band 212, Springer-Verlag, New York-Heidelberg, 1975. MR 0385836
Kisuke Tsuchida, Principal cofibrations, Tohoku Math. J. (2) 16 (1964), 321–333. MR 177415, DOI 10.2748/tmj/1178243643
K. Varadarajan, Generalised Gottlieb groups, J. Indian Math. Soc. (N.S.) 33 (1969), 141–164 (1970). MR 281207