Talk:Spin bordism

Latest revision as of 17:05, 19 March 2019

Throughout section $There seems to be an issue in section 4.2, in particular 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: 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. $M_J$ should be $N_J$. If this is the case, then the fifth dot point is no longer needed (just take $k = 0$).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 $\Omega^{Spin}_*\otimes\mathbb{Z}_2$. 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:

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. $M_J$ should be $N_J$. If this is the case, then the fifth dot point is no longer needed (just take $k = 0$).