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The order of the Hopf bundle on projective Stiefel manifolds

100%

Sankaran P., Zvengrowski P.

Fundamenta Mathematicae

1999

tom 161

nr 1-2

225-233

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.

Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians

81%

Lakshmibai V., Raghavan K., Sankaran P.

Open Mathematics

2009

tom 7

nr 2

214-223

It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Open Mathematics

2 Sankaran P.

1 Lakshmibai V.

1 Raghavan K.

1 Zvengrowski P.

1 2009

1 1999

Wyniki wyszukiwania

The order of the Hopf bundle on projective Stiefel manifolds

Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians