The order of the Hopf bundle on projective Stiefel manifolds
Fundamenta Mathematicae, Tome 161 (1999) no. 1, pp. 225-233
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Affiliations des auteurs :
Parameswaran Sankaran 1 ; Peter Zvengrowski 1
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author = {Parameswaran Sankaran and Peter Zvengrowski},
title = {The order of the {Hopf} bundle on projective {Stiefel} manifolds},
journal = {Fundamenta Mathematicae},
pages = {225--233},
publisher = {mathdoc},
volume = {161},
number = {1},
year = {1999},
doi = {10.4064/fm_1999_161_1-2_1_225_233},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm_1999_161_1-2_1_225_233/}
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Parameswaran Sankaran; Peter Zvengrowski. The order of the Hopf bundle on projective Stiefel manifolds. Fundamenta Mathematicae, Tome 161 (1999) no. 1, pp. 225-233. doi: 10.4064/fm_1999_161_1-2_1_225_233
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