Talk:Spin bordism
From Manifold Atlas
(Difference between revisions)
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− | Throughout section $4.2$, we should still have the condition that | + | <wikitex> |
+ | Throughout section $4.2$, we should still have the condition that $J$ doesn't contain $1$. Right? | ||
− | There also seems to be an issue with the basis for | + | There also seems to be an issue with the basis for $\Omega^{Spin}_*\otimes\mathbb{Z}_2$. The third dot point reads "$M_J\times\omega_8^k$ with $k \geq 0$, $n(J)$ odd". But $M_J$ is only defined for $n(J)$ even. |
I can think of two possibilities of what was meant: | I can think of two possibilities of what was meant: | ||
− | 1. " | + | 1. "$n(J)$ odd" should be "$n(J)$ even". If this was what was intended, then this is covered by the first dot point with $i = 0$ so the third dot point is unnecessary. |
− | 2. | + | 2. $M_J$ should be $N_J$. If this is the case, then the fifth dot point is no longer needed (just take $k = 0$). |
+ | </wikitex> |
Latest revision as of 17:05, 19 March 2019
Throughout section , we should still have the condition that doesn't contain . Right?
There also seems to be an issue with the basis for . The third dot point reads " with , odd". But is only defined for even.
I can think of two possibilities of what was meant:
1. " odd" should be " even". If this was what was intended, then this is covered by the first dot point with so the third dot point is unnecessary.
2. should be . If this is the case, then the fifth dot point is no longer needed (just take ).