How to calculate the 3-local Coker of map $\pi_{11}(Sp(3))\overset{{\alpha_1(11)}^* \oplus {\alpha_2(11)}^*}\longrightarrow \pi_{14}(Sp(3))\oplus \pi_{18}(Sp(3))$? where $\pi_{11}(Sp(3))\cong \mathbb{Z}$ , $\pi_{14}(Sp(3))\cong \mathbb{Z}_9$ and $\pi_{18}(Sp(3))\cong \mathbb{Z}_{27}$. That is we need to 3-local Coker of the map $\mathbb{Z} \overset{{\alpha_1(11)}^* \oplus {\alpha_2(11)}^*}\longrightarrow \mathbb{Z}_9\oplus \mathbb{Z}_{27}$. Thank you so much for your reply.
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2$\begingroup$ What's that map? How is it defined? $\endgroup$– Fernando MuroCommented May 16, 2023 at 7:37
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$\begingroup$ The maps $\alpha_1(11)^*: \pi_{11}(Sp(3))\rightarrow \pi_{14}(Sp(3)) $ and $\alpha_2(11)^*: \pi_{11}(Sp(3))\rightarrow \pi_{18}(Sp(3)) $ are define naturality, where $\alpha_1(11): S^{14}\rightarrow S^{11}$ and $\alpha_2(11): S^{18}\rightarrow S^{11}$ are Toda notations. $\endgroup$– Sajjad MohammadiCommented May 16, 2023 at 14:39
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$\begingroup$ Where can one find the definitions of Toda notations? $\endgroup$– Fernando MuroCommented May 16, 2023 at 16:08
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$\begingroup$ COMPOSITION METHODS IN HOMOTOPY GROUPS OF SPHERES, BY Hirosi Toda PRINCETON, NEW JERSEY PRINCETON UNIVERSITY PRESS 1962 $\endgroup$– Sajjad MohammadiCommented May 17, 2023 at 4:38
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