Stiefel manifolds as framed boundaries (Q919673)

This paper proves that the Stiefel manifolds \(V_{n,q}\) of orthogonal q- frames in \(F^ n\), \(F={\mathbb{R}}\), \({\mathbb{C}}\), or \({\mathbb{H}}\) (with \(q\leq n- 1\), n-1, or n) are framed boundaries. This result depends on the choice of framing; the framing used is the natural one, and thinking of \(V_{n,q}\) as a sphere bundle, the framing extends over the corresponding disc bundle.