Cohomology rings of oriented Grassmann manifolds \(\widetilde G_{2^t,4}\)

Cohomology rings of oriented Grassmann manifolds \(\widetilde G_{2^t,4}\)

We give a description of the mod 2 cohomology algebra of the oriented Grassmann manifold \(\widetilde G_{2^t,4}\) as the quotient of a polynomial algebra by a certain ideal. In the process we find a Gr\"obner basis for that ideal, which we then use to exhibit an additive basis for \(H^*(\wideti...

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Veröffentlicht in:arXiv.org 2024-10
Hauptverfasser: Colović, Uroš A, Jovanović, Milica, Prvulović, Branislav I
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Homology
Manifolds (mathematics)
Polynomials
Rings (mathematics)
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Zusammenfassung:We give a description of the mod 2 cohomology algebra of the oriented Grassmann manifold \(\widetilde G_{2^t,4}\) as the quotient of a polynomial algebra by a certain ideal. In the process we find a Gr\"obner basis for that ideal, which we then use to exhibit an additive basis for \(H^*(\widetilde G_{2^t,4};\mathbb Z_2)\).
ISSN:2331-8422