The order of the Hopf bundle on projective Stiefel manifolds

Parameswaran Sankaran¹ ; Peter Zvengrowski¹

¹

Fundamenta Mathematicae, Tome 161 (1999) no. 1, pp. 225-233.

Résumé

The projective Stiefel manifold $X_{n,k}$ has a canonical line bundle $ξ_{n,k}$, called the Hopf bundle. The order of $cξ_{n,k}$, the complexification of $ξ_{n,k}$, as an element of (the abelian group) $K(X_{n,k})$, has been determined in [3], [5], [6]. The main result in the present work is that this order equals the order of $ξ_{n,k}$ itself, as an element of $KO(X_{n,k})$, for $n ≡ 0,± 1 (mod 8), or for k in the "upper range for n" (approximately $k ≥ n/2$). Certain applications are indicated.

Détail

DOI : 10.4064/fm_1999_161_1-2_1_225_233