On framed cobordism classes of classical Lie groups

Abstract

It is known that any compact connected Lie group with its left invariant framing is framed null-cobordant in the p-component for any prime p≠2,3. In this paper we will prove that the 3-components of SO2n+1 and Sp(n) are zero for n≥3, n≠5,7,11. Combining this with the previously known results on SO2n and SU(n) consequently we see that any classical group has at most only the 2-component with some exceptions.