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Aug 10, 2018 at 11:39 vote accept ARG
Aug 9, 2018 at 18:37 comment added ARG How nice! and thanks for correcting my misunderstanding of the obstruction class... It was based on the idea the values of both the Euler and Pontryagin classes can be identifies with $\mathbb{Z}$ and that there is no other class in this dimension. So I (wrongly, hastily and naively) assumed there could be no other way to express the obstruction class. Should I edit the question?
Aug 9, 2018 at 15:46 history answered Matthias Wendt CC BY-SA 4.0