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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the cohomology of real Grassmanians


Author: Howard L. Hiller
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1980-0552272-2
Article copyright: © Copyright 1980 American Mathematical Society