The fibre-bundles tag has no wiki summary.

**0**

votes

**0**answers

185 views

### Lifting a quadratic system to a non vanishing vector field on $S^{3}$ or $T^{1} S^{2}$

Let $P:S^{3}\to S^{2}$ be the Hopf fibration. For a vector field $X$ on $S^{2}$ there is a non vanishing vector field $\tilde{X}$ on $S^{3}$ such that $DP(\tilde{X})=X$. It is constructed in ...

**14**

votes

**4**answers

1k views

### What is a section?

This question comes out of the answers to Ho Chung Siu's question about vector bundles. Based on my reading, it seems that the definition of the term "section" went through several phases of ...

**17**

votes

**3**answers

903 views

### Cohomology of fibrations over the circle: how to compute the ring structure?

This question is inspired by Cohomology of fibrations over the circle Moreover, it can be considered a subquestion of the above, but somehow it seems to me that some of the more interesting points ...

**14**

votes

**1**answer

1k views

### Which principlal bundles are locally trivial?

If $H$ is a closed subgroup of a topological group $G$, then the orbit map $G\to G/H$ is a principal bundle, yet somewhat surprisingly, it need not be locally trivial.
In the wikipedia article on ...