Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

$K$-theory of projective Stiefel manifolds


Authors: Nelza E. Barufatti and Derek Hacon
Journal: Trans. Amer. Math. Soc. 352 (2000), 3189-3209
MSC (1991): Primary 55N15; Secondary 55R25, 57T15
DOI: https://doi.org/10.1090/S0002-9947-00-02614-3
Published electronically: March 27, 2000
MathSciNet review: 1709770
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

Using the Hodgkin spectral sequence we calculate $K^{*}(X_{m,k})$, the complex $K$-theory of the projective Stiefel manifold $X_{m,k}$, for $mk$even. For $mk$ odd, we are only able to calculate $K^{0}(X_{m,k})$, but this is sufficient to determine the order of the complexified Hopf bundle over $ X_{m,k}$.


References [Enhancements On Off] (What's this?)

  • 1. Adams, J.F. - Vector Fields on Spheres, Ann. of Math., 75 (1962), 603-632. MR 25:2614
  • 2. Antoniano, E., Gitler, S., Ucci, J. and Zvengrowski, P. - On the $K$-theory and parallelizability of projective Stiefel manifolds, Boletin de la Sociedad Matemática Mexicana, (1986), 29-116. MR 89g:57058
  • 3. Barufatti, N. - Obstructions to immersions of projective Stiefel manifolds, Contemp. Math., AMS, vol. 161 (1994), pp. 281-287. MR 95c:57049
  • 4. Bröcker, T. and tom Dieck, T. -Representations of compact Lie groups, G.T.M., Springer-Verlag (1985). MR 86i:22023
  • 5. Cartan, H. and Eilenberg, S. - Homological Algebra, Princeton University Press (1956). MR 17:1040e
  • 6. Gitler, S. and Handel, D. - The projective Stiefel manifolds I, Topology 7, (1968), 39-46. MR 36:3373a
  • 7. Gitler, S. and Lam, K. Y. - The K-theory of Stiefel manifolds, Lecture Notes in Math., vol. 168, Springer-Verlag, 168 (1970), pp. 35-66. MR 43:1223
  • 8. Gould, H. W. - Combinatorial Identities, Morgantown Printing, Morgantown, W. Va. (1972). MR 50:5879
  • 9. Held, R. P. and Suter, U. - Stable vector bundles over the projective orthogonal groups, Comm. Math. Helv., 50 (1975), 93-114. MR 51:4246
  • 10. Hodgkin, L. - The equivariant Künneth theorem in K-theory, Lectures Notes in Math., vol. 496, Springer -Verlag, 496 (1975), pp. 1-101. MR 57:17645
  • 11. Husemoller, D. - Fibre Bundles, McGraw-Hill, New York (1966). MR 37:4821
  • 12. Roux, A. - Application de la suite spectrale d'Hodgkin au calcul de la K-théorie des variétés de Stiefel, Bull. Soc. Math. France, 99 (1971), 345-368. MR 47:1057

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 55N15, 55R25, 57T15

Retrieve articles in all journals with MSC (1991): 55N15, 55R25, 57T15


Additional Information

Nelza E. Barufatti
Affiliation: Instituto Politécnico, UERJ, Caixa Postal 97282, CEP: 28601-970, Nova Friburgo, RJ, Brasil
Email: nelza@iprj.uerj.br

Derek Hacon
Affiliation: PUC-RJ, Departamento de Matemática, R. Marquês de São Vicente, 225, Gávea, Rio de Janeiro, RJ, Brasil, CEP:22453-900
Email: derek@mat.puc-rio.br

DOI: https://doi.org/10.1090/S0002-9947-00-02614-3
Received by editor(s): May 27, 1993
Published electronically: March 27, 2000
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society