Transactions of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

-theory of projective Stiefel manifolds

Author(s): Nelza E. Barufatti; Derek Hacon
Journal: Trans. Amer. Math. Soc. 352 (2000), 3189-3209.
MSC (1991): Primary 55N15; Secondary 55R25, 57T15
Posted: March 27, 2000
MathSciNet review: 1709770
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

Using the Hodgkin spectral sequence we calculate $K^{*}(X_{m,k})$ , the complex -theory of the projective Stiefel manifold $X_{m,k}$ , for even. For 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:

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 -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

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|