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

Re Answers: do we know the positive answer for all relevant $n > 8$$<wikitex>; Re Answers: do we know the positive answer for all relevant $n > 8$, or just some. i.e. if $n > 8$ with $\pi_n(BO) \neq 0$ can the obstruction to lifting a $BO\langle n-1\rangle$ structure to $BO\langle n \rangle$ depend upon the choice of $BO \langle n-1 \rangle$ structure? </wikitex>n > 8$, or just some. i.e. if $n > 8$$n > 8$ with $\pi_n(BO) \neq 0$$\pi_n(BO) \neq 0$ can the obstruction to lifting a $BO\langle n-1\rangle$$BO\langle n-1\rangle$ structure to $BO\langle n \rangle$$BO\langle n \rangle$ depend upon the choice of $BO \langle n-1 \rangle$$BO \langle n-1 \rangle$ structure?