Abstract
For \(n\in \{2^t-3,2^t-2,2^t-1\}\) \((t\ge 3)\) we study the cohomology algebra \(H^*(\widetilde{G}_{n,3};{\mathbb {Z}}_2)\) of the Grassmann manifold \(\widetilde{G}_{n,3}\) of oriented 3-dimensional subspaces of \({\mathbb {R}}^n.\) A complete description of \(H^*(\widetilde{G}_{n,3};{\mathbb {Z}}_2)\) is given in the cases \(n=2^t-3\) and \(n=2^t-2,\) while in the case \(n=2^t-1\) we obtain a description complete up to a coefficient from \({\mathbb {Z}}_2.\)
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Communicated by Haynes Miller.
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M. Jovanović was partially supported by the Science Fund of the Republic of Serbia, Grant no. 7749891, Graphical Languages—GWORDS. B. I. Prvulović was partially supported by the Ministry of Science, Technological Development and Innovations of the Republic of Serbia [Contract no. 451-03-47/2023-01/200104].
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Jovanović, M., Prvulović, B.I. On the mod 2 cohomology algebra of oriented Grassmannians. J. Homotopy Relat. Struct. (2024). https://doi.org/10.1007/s40062-024-00350-9
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DOI: https://doi.org/10.1007/s40062-024-00350-9