Talk:Does the existence of a string structure depend on a spin structure ? (and a generalization)

From Manifold Atlas
Jump to: navigation, search

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?

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.

Personal tools
Namespaces
Variants
Actions
Navigation
Interaction
Toolbox