Talk:Spin bordism
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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? | + | Throughout section $4.2$, we should still have the condition that <math>J</math> doesn't contain <math>1</math>. 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 <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. | ||
Revision as of 17:02, 19 March 2019
Throughout section $4.2$, we should still have the condition that Failed to parse (Missing texvc executable; please see math/README to configure.): J
doesn't contain Failed to parse (Missing texvc executable; please see math/README to configure.): 1
. Right?
There also seems to be an issue with the basis for Failed to parse (Missing texvc executable; please see math/README to configure.): \Omega^{Spin}_*\otimes\mathbb{Z}_2 . The third dot point reads "Failed to parse (Missing texvc executable; please see math/README to configure.): M_J\times\omega_8^k
with Failed to parse (Missing texvc executable; please see math/README to configure.): k \geq 0
, Failed to parse (Missing texvc executable; please see math/README to configure.): n(J)
odd". But Failed to parse (Missing texvc executable; please see math/README to configure.): M_J is only defined for Failed to parse (Missing texvc executable; please see math/README to configure.): n(J) even.
I can think of two possibilities of what was meant:
1. "Failed to parse (Missing texvc executable; please see math/README to configure.): n(J)
odd" should be "Failed to parse (Missing texvc executable; please see math/README to configure.): n(J) even". If this was what was intended, then this is covered by the first dot point with Failed to parse (Missing texvc executable; please see math/README to configure.): i = 0 so the third dot point is unnecessary.
2. Failed to parse (Missing texvc executable; please see math/README to configure.): M_J
should be Failed to parse (Missing texvc executable; please see math/README to configure.): N_J
. If this is the case, then the fifth dot point is no longer needed (just take Failed to parse (Missing texvc executable; please see math/README to configure.): k = 0 ).
