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 $n > 9$, or just some. i.e. if $n > 9$ 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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