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Let $p:B\to BO$ be a fibration. We say that a manifold has a $B$-structure if its stable tangent bundle lifts to $B$. I am interested in the question of whether there exists, for a given even ...

A famous result by Thom states that Oriented Bordism classes are determined by characteristic numbers; specifically, two closed manifolds are orientedly bordant if and only if they have the same ...