In my mind it is clear the formal definition of a fiber bundle but I can not have a geometric image of it. Roughly speaking, given three topological spaces $X, B, F$ with a continuous surjection $\pi: X\rightarrow B$, we “attach” to every point $b$ of $B$ a closed set $\pi^{-1}(b)$ such that it is […]

In this question I am using Wiki’s definitions for fibration and fiber bundle. I want to be general in asking my question, but I am mostly interested in smooth compact manifolds and smooth fibrations and bundle projection between them. Under some mild topological assumption on the base space (of course verified in the case of […]

I’m interested in understanding the importance of the local coefficients in the definition of the obstruction cocycle for a lift of a map $f\colon X \to B$ along a fibration $p \colon E \to B$. I’m following the explanation given at page $189$ in Davis & Kirk’s Lecture Notes in Algebraic Topology. Aim of this […]

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