
For a compact simple Lie group $G$, we show that the element $[G, \mathcal{L}] \in \pi^S_*(S^0)$ represented by the pair $(G, \mathcal{L})$ is zero, where $\mathcal{L}$ denotes the left invariant framing of $G$. The proof relies on the method of E. Ossa [Topology, 21 (1982), 315–323].
19L20, Lie groups, Adams conjecture, 57R15, 22E46, framed manifolds
19L20, Lie groups, Adams conjecture, 57R15, 22E46, framed manifolds
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