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The null-cobordantness of a framed compact connected Lie group G has been discussed in [7] and many other papers. As is well known, the left (or right) invariant tangent fields over G yield a trivialization of its tangent bundle and so induce a framing of the stable normal bundle of G in a canonical way. This defines an element, denoted simply by [G], of the stable homotopy group π ∗ of spheres via the Pontrjagin–Thom construction. The vanishing of [G] means, of course, that such a framed Lie group G is null-cobordant. Ossa [7] has shown the following result of a general nature: 8 · 32[G] = 0.

A REMARK ON THE FRAMED NULL-COBORDANTNESS OF THE EXCEPTIONAL LIE GROUP E6

A REMARK ON THE FRAMED NULL-COBORDANTNESS OF THE EXCEPTIONAL LIE GROUP E₆