PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 161 | 1-2 | 225-233
Tytuł artykułu

The order of the Hopf bundle on projective Stiefel manifolds

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
161
Numer
1-2
Strony
225-233
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-11-23
poprawiono
1998-07-04
Twórcy
  • Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada
Bibliografia
  • [1] Adams, J. F., Vector fields on spheres, Ann. of Math. 75 (1962), 603-632.
  • [2] Adams, J. F., Lectures on Lie Groups, Univ. Chicago Press, Midway reprint, 1982.
  • [3] Antoniano, E., Gitler, S., Ucci, J., and Zvengrowski, P., On the K-theory and parallelizability of projective Stiefel manifolds, Bol. Soc. Mat. Mexicana 31 (1986), 29-46.
  • [4] Atiyah, M. F., and Hirzebruch, F., Vector bundles and homogeneous spaces, in: Proc. Sympos. Pure Math. 3, Amer. Math. Soc., 1961, 7-38.
  • [5] Barufatti, N., Obstructions to immersions of projective Stiefel manifolds, in: Contemp. Math. 161, Amer. Math. Soc., 1994, 281-287.
  • [6] Barufatti, N., and Hacon, D., K-theory of projective Stiefel manifolds, to appear.
  • [7] Gitler, S., and Handel, D., The projective Stiefel manifolds - I, Topology 7 (1968), 39-46.
  • [8] Hodgkin, L., The equivariant Künneth theorem in K-theory, in: Lecture Notes in Math. 496, Springer, 1969, 1-101.
  • [9] Husemoller, D., Fibre Bundles, 2nd ed., Grad. Texts in Math. 20, Springer, 1975.
  • [10] Korbaš, J., and Zvengrowski, P., On sectioning tangent bundles and other vector bundles, Rend. Circ. Mat. Palermo (2) Suppl. 39 (1996), 85-104.
  • [11] Lam, K. Y., A formula for the tangent bundle of flag manifolds and related manifolds, Trans. Amer. Math. Soc. 213 (1975), 305-314.
  • [12] Milnor, J., and Stasheff, J., Characteristic Classes, Ann. of Math. Stud. 76, Princeton Univ. Press, Princeton, 1974.
  • [13] Pittie, H. V., Homogeneous vector bundles on homogeneous spaces, Topology 11 (1972), 199-204.
  • [14] Smith, L., Some remarks on projective Stiefel manifolds, immersions of projective spaces, and spheres, Proc. Amer. Math. Soc. 80 (1980), 663-669.
  • [15] P. Zvengrowski et al., The order of line bundles, preprint.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv161i1p225bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.