All Questions

RECAP on classification of bundles We want to classify $G$-principal bundles over $X$ (smooth manifold, G compact Lie). These are in 1-1 correspondence with homotopy classes of maps $[X,BG]$ (where $...

Let $\pi \colon E \to X$ be a fiber bundle with fiber $F$ and suppose that $\tilde H^i(F) = 0$ for $0 \leq i \leq k-1$. Using the Leray-Serre spectral sequence, we get an exact sequence $$ 0 \to H^k(...

Let $p:E \to X$ be a fibration with the fiber $F$ where $X$ is a CW-complex. Denote by $U$ the set $U:=D^n \times \{0\} \cup S^{n-1} \times I$ (part of a cylinder) and let $\tilde{f}:U \to E$ be a ...

I think this question is related to what is known as "obstruction theory", but I'm not very familiar with this field of mathematics, so I am asking here. Let $\pi:N\rightarrow M$ be a smooth ...