# Tagged Questions

**0**

votes

**0**answers

152 views

### Does every real vector bundle admit a metric?

Let $ E \longrightarrow B $ be a vector bundle.
I know that if B is paracompact, the bundle admits a metric.
My question is the following: is this true for any B?
I also know that a reduction of ...

**1**

vote

**2**answers

1k views

### Vector bundles vs principal $G$-bundles

It is well known that a (real) vector bundle $\pi : E\to B$ over a topological space (or manifold) $B$ is a fibre bundle whose fibres
$$F=\pi^{-1}(x), \ \ \ x\in B $$
over any $x\in B$, are ...

**2**

votes

**1**answer

225 views

### family of torsors and family of vector bundles

Suppose $X$ and $Y$ are smooth connected schemes over a field $k=\bar{k}$, $f: X\times_kY\to X$ is the first projection. You may assume $Y$ is proper if you like, my question is if $P\to X\times_kY$ ...

**8**

votes

**2**answers

879 views

### Nice example of a topologically trivial bundle with nontrivial connection

So, I've been trying to understand what exactly an anomaly is, and how they arise in physics. Apparently an anomalous theory is some theory whose action is given by a section of some bundle (rather ...

**2**

votes

**0**answers

653 views

### Vector bundles on some non-projective surfaces

Let $X$ be a smooth projective curve over a field $k$ and let $L$ be a line bundle on $X$.
I will denote by $S$ the total space of $L$ -- this is a smooth surface over $k$ containing
$X$ (as the zero ...

**3**

votes

**6**answers

1k views

### Reference request: Moduli spaces of bundles over singular curves

I would like to know some reference (articles, books...) about any kind of moduli spaces of any of the following objects:
vector bundles
torsion-free sheaves
principal bundles
parabolic bundles
...

**3**

votes

**1**answer

680 views

### Principal bundles and associated vector bundles, the case of the complex projective space (1,0)-forms

As can be guessed from some of my previous questions, I'm trying to understand, at the moment, the relationship between principal and their associated vector bundles. To this end I've been looking at ...

**1**

vote

**4**answers

352 views

### Local Triviality of an Associated Bundle

I was reading this question link text
and can't seem to see why, if $\pi: P \to B$ is a principle $G$-bundle and $$\rho:G \to GL_n(\mathbb{C})$$ is a representation of $G$, then the total space $P ...