Talk:Spin bordism

Revision as of 17:02, 19 March 2019 (view source) Michael Albanese (Talk | contribs) ← Older edit		Latest revision as of 17:05, 19 March 2019 (view source) Michael Albanese (Talk | contribs)
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−	Throughout section $4.2$, we should still have the condition that <math>J</math> doesn't contain <math>1</math>. Right?	+	<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 <math>\Omega^{Spin}_*\otimes\mathbb{Z}_2</math>. The third dot point reads "<math>M_J\times\omega_8^k</math> with <math>k \geq 0</math>, <math>n(J)</math> odd". But <math>M_J</math> is only defined for <math>n(J)</math> even.	+	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. "<math>n(J)</math> odd" should be "<math>n(J)</math> even". If this was what was intended, then this is covered by the first dot point with <math>i = 0</math> so the third dot point is unnecessary.	+	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. <math>M_J</math> should be <math>N_J</math>. If this is the case, then the fifth dot point is no longer needed (just take <math>k = 0</math>).	+	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>

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Latest revision as of 17:05, 19 March 2019

Throughout section $<wikitex> Throughout section .2$, we should still have the condition that $J$ doesn't contain 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 $k = 0$).

$. 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 $k = 0$). 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 $k = 0$).