The order of the Hopf bundle on projective Stiefel manifolds

• Autorzy: Parameswaran Sankaran , Peter Zvengrowski
• 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.

Kategorie tematyczne

• 57T15: Homology and cohomology of homogeneous spaces of Lie groups
• 55N15: K -theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 161
• Numer: 1-2
• Strony: 225-233

Daty

wydano

1999

otrzymano

1997-11-23

poprawiono

1998-07-04

Twórcy

autor

Parameswaran Sankaran

• SPIC Mathematical Institute, 92 G.N. Chetty Road, Chennai 600 017, India,

autor

Peter Zvengrowski

• Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada

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