All Questions

In Theorem 2 of these notes, Ralph Cohen reformulates the main theorem of Hirsch-Smale theory merely in terms of normal bundles. In particular, he says that if $N, M$ are two manifolds, $\dim N< ...

Description I noticed a repeating theme in vector bundle theory, and wonder if there's a theorem that describes this kind of phenomenon. Given a vector bundle $E$ over a manifold $X$. If there is a ...

Let $E$ be an $n$-plane bundle over CW complex $X$. Then $E$ is a pullback of tautological bundle $\gamma_n$ over $BO(n)$ i.e. $E=f^*(\gamma_n)$. This $f$ is called classyfing map. One can show that ...