Abstract
A study is made of the action of the fundamental group of a bouquet of a circle and a 1-connected space on the higher homotopy groups. If the 1-connected space is a suspension space, it is shown, with the aid of a theorem of Hartley on wreath products of groups and the Hilton-Milnor theorem, that the action is residually nilpotent. An unsuccessful approach in the case of a general 1-connected space is discussed, as it has some interesting features.
Citation
Joseph Roitberg. "Note on the homotopy groups of a bouquet $S^1\vee Y$, $Y$ 1-connected." Homology Homotopy Appl. 16 (1) 83 - 87, 2014.
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