On the cohomology of real Grassmanians
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- by Howard L. Hiller PDF
- Trans. Amer. Math. Soc. 257 (1980), 521-533 Request permission
Abstract:
Let ${G_k}({\textbf {R}^{n + k}})$ denote the grassman manifold of k-planes in real $(n + k)$-space and ${w_1} \in {H^1}({G_k}({\textbf {R}^{n + k}}); {\textbf {Z}_2})$ the first Stiefel-Whitney class of the universal bundle. Using Schubert calculus techniques and the cohomology of flag manifolds we estimate the height of ${w_1}$ in the cohomology ring. We then apply this to improve earlier lower bounds on the Lusternik-Schnirelmann category of real grassmanians.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 257 (1980), 521-533
- MSC: Primary 14M15; Secondary 55R40, 57T15
- DOI: https://doi.org/10.1090/S0002-9947-1980-0552272-2
- MathSciNet review: 552272