On framed simple Lie groups

Abstract

For a compact simple Lie group G, we show that the element [G, ℒ] ∈ π^S_*(S⁰) represented by the pair (G, ℒ) is zero, where ℒ denotes the left invariant framing of G. The proof relies on the method of E. Ossa [Topology, 21 (1982), 315–323].