On the height of the first Stiefel-Whitney class
HTML articles powered by AMS MathViewer
- by Howard L. Hiller PDF
- Proc. Amer. Math. Soc. 79 (1980), 495-498 Request permission
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.References
- Shiing-shen Chern, On the multiplication in the characteristic ring of a sphere bundle, Ann. of Math. (2) 49 (1948), 362–372. MR 24127, DOI 10.2307/1969285
- Howard L. Hiller, On the cohomology of real Grassmanians, Trans. Amer. Math. Soc. 257 (1980), no. 2, 521–533. MR 552272, DOI 10.1090/S0002-9947-1980-0552272-2 V. Opriou, Some non-embedding theorems for the grassmann manifolds, ${G_{2,n}}$ and ${G_{3,n}}$, Proc. Edinburgh Math. Soc. 20 (1977), 177-185.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 495-498
- MSC: Primary 57T15; Secondary 55R40, 57R20
- DOI: https://doi.org/10.1090/S0002-9939-1980-0568001-8
- MathSciNet review: 568001