Talk:Does the existence of a string structure depend on a spin structure ? (and a generalization)
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| − | Re Answers: do we know the positive answer for all relevant $n > | + | Re Answers: do we know the positive answer for all relevant $n > 8$, or just some. i.e. if $n > 8$ with $\pi_n(BO) \neq 0$ can the obstruction to lifting a $BO\langle n-1\rangle$ structure to $BO\langle n \rangle$ depend upon the choice of $BO \langle n-1 \rangle$ structure? |
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| + | This is answered now too by a mod 2 consideration and Stong's paper. I believe the mod 3 consideration works for all multiples of 4. Interestingly, modulo bigger primes seems it seems to hold that the obstructions to lifting from | ||
| + | $BO\langle n\rangle $ to $BO\langle n+4\rangle $ are equal if the $BO\langle n-4\rangle $-structure is the same, | ||
| + | but can be different if one only knows that the $BO\langle n-2p+2 \rangle$-structure is the same. | ||
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Latest revision as of 17:25, 21 January 2011
Re Answers: do we know the positive answer for all relevant 
, or just some. i.e. if with 
can the obstruction to lifting a 
structure to 
depend upon the choice of 
structure?
This is answered now too by a mod 2 consideration and Stong's paper. I believe the mod 3 consideration works for all multiples of 4. Interestingly, modulo bigger primes seems it seems to hold that the obstructions to lifting from
to 
are equal if the 
-structure is the same,
but can be different if one only knows that the 
-structure is the same.
