Timeline for Examples of manifolds with first nontrivial SW-class in degree 16 or bigger
Current License: CC BY-SA 4.0
3 events
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| Jul 25, 2022 at 15:59 | comment | added | Arun Debray | The total Stiefel-Whitney class of $\mathbb{RP}^k$ is $(1+x)^{k+1}$, where $x$ is the generator of $H^1(\mathbb{RP}^k; \mathbb Z/2)$. So when $k = 2^{t+1} + 2^t - 1$, $T\mathbb{RP}^k$ has type $t$. Is this the sort of example you had in mind? | |
| Jul 18, 2022 at 17:22 | comment | added | Mark Grant | Renee Hoekzema has done some work related to this, see e.g. people.math.rochester.edu/faculty/doug/otherpapers/Hoekzema.pdf where the Rosenfeld plane $(\mathbb{O}\otimes\mathbb{H})\mathbb{P}^2$ is discussed as a candidate of a manifold of type $4$ (it has type at least $4$ as far as I understood). | |
| Jul 18, 2022 at 16:28 | history | asked | Jens Reinhold | CC BY-SA 4.0 |