Heights of Stiefel--Whitney classes and zero-divisor cup-length of some Grassmann manifolds
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910057930686464 |
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| author | Jovanović, Milica Ovaskainen, Vuk Prvulović, Branislav I. Subotić, Antonije |
| author_facet | Jovanović, Milica Ovaskainen, Vuk Prvulović, Branislav I. Subotić, Antonije |
| contents | We calculate the heights of Stiefel--Whitney classes of the canonical vector bundle over the oriented Grassmannians $\widetilde G_{n,4}\cong SO(n)/(SO(4)\times SO(n-4))$ in the cases $n\in\{2^t-2,2^t-1,2^t,2^t+1\}$, $t\ge4$. Using some additional computations in modulo $2$ cohomology of $\widetilde G_{n,4}$ and the well-known connection between topological complexity and zero-divisor cup-length, we obtain lower bounds for topological complexity of these Grassmannians. We also extend recent results of Rusin, who computed the modulo $2$ cup-length of $\widetilde G_{n,4}$ for $n\in\{2^t-2,2^t-1,2^t\}$, to the case $n=2^t+1$, $t\ge3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17660 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Heights of Stiefel--Whitney classes and zero-divisor cup-length of some Grassmann manifolds Jovanović, Milica Ovaskainen, Vuk Prvulović, Branislav I. Subotić, Antonije Algebraic Topology Primary 55R40, 55M30, Secondary 13P10 We calculate the heights of Stiefel--Whitney classes of the canonical vector bundle over the oriented Grassmannians $\widetilde G_{n,4}\cong SO(n)/(SO(4)\times SO(n-4))$ in the cases $n\in\{2^t-2,2^t-1,2^t,2^t+1\}$, $t\ge4$. Using some additional computations in modulo $2$ cohomology of $\widetilde G_{n,4}$ and the well-known connection between topological complexity and zero-divisor cup-length, we obtain lower bounds for topological complexity of these Grassmannians. We also extend recent results of Rusin, who computed the modulo $2$ cup-length of $\widetilde G_{n,4}$ for $n\in\{2^t-2,2^t-1,2^t\}$, to the case $n=2^t+1$, $t\ge3$. |
| title | Heights of Stiefel--Whitney classes and zero-divisor cup-length of some Grassmann manifolds |
| topic | Algebraic Topology Primary 55R40, 55M30, Secondary 13P10 |
| url | https://arxiv.org/abs/2603.17660 |