On the mod 2 cohomology algebra of oriented Grassmannians
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914412381601792 |
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| author | Jovanović, Milica Prvulović, Branislav I. |
| author_facet | Jovanović, Milica Prvulović, Branislav I. |
| contents | For $n\in\{2^t-3,2^t-2,2^t-1\}$ ($t\ge3$) 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 $\mathbb Z_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11153 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the mod 2 cohomology algebra of oriented Grassmannians Jovanović, Milica Prvulović, Branislav I. Algebraic Topology Primary 55R40, Secondary 13P10 For $n\in\{2^t-3,2^t-2,2^t-1\}$ ($t\ge3$) 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 $\mathbb Z_2$. |
| title | On the mod 2 cohomology algebra of oriented Grassmannians |
| topic | Algebraic Topology Primary 55R40, Secondary 13P10 |
| url | https://arxiv.org/abs/2306.11153 |