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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 257 (1980), 521-533
  • MSC: Primary 14M15; Secondary 55R40, 57T15
  • DOI:
  • MathSciNet review: 552272