Characteristic rank of vector bundles over Stiefel manifolds

Abstract

The characteristic rank of a vector bundle ξ over a finite connected CW-complex X is by definition the largest integer \({k, 0 \leq k \leq \mathrm{dim}(X)}\) , such that every cohomology class \({x \in H^{j}(X;\mathbb{Z}_2), 0 \leq j \leq k}\) , is a polynomial in the Stiefel–Whitney classes w i (ξ). In this note we compute the characteristic rank of vector bundles over the Stiefel manifold \({V_k(\mathbb{F}^n), \mathbb{F} = \mathbb{R}, \mathbb{C}, \mathbb{H}}\) .

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Correspondence to Ajay Singh Thakur.

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Part of this research was carried out while J. Korbaš was a member of two research teams supported in part by the grant agency VEGA (Slovakia).

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Korbaš, J., Naolekar, A.C. & Thakur, A.S. Characteristic rank of vector bundles over Stiefel manifolds. Arch. Math. 99, 577–581 (2012). https://doi.org/10.1007/s00013-012-0454-3

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Mathematics Subject Classification (2010)

  • 57R20
  • 57T15

Keywords

  • tiefel–Whitney class
  • Characteristic rank
  • Stiefelmanifold