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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the height of the first Stiefel-Whitney class


Author: Howard L. Hiller
Journal: Proc. Amer. Math. Soc. 79 (1980), 495-498
MSC: Primary 57T15; Secondary 55R40, 57R20
MathSciNet review: 568001
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Abstract: Let $ {G_k}({{\mathbf{R}}^{n + k}})$ denote the grassmann manifold of k-planes in real $ (n + k)$-space and $ {w_1} \in {H^1}({G_k}({{\mathbf{R}}^{n + k}});{{\mathbf{Z}}_2})$ the first Stiefel-Whitney class of the universal bundle. We determine, for many (k, n), the exact height of $ {w_1}$ in the cohomology ring. We also indicate the combinatorial significance of the complex analogue of these computations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0568001-8
PII: S 0002-9939(1980)0568001-8
Article copyright: © Copyright 1980 American Mathematical Society