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In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. If the fiber bundle is a vector bundle, then the notion of parallel transport must be linear. Such a connection is equivalently specified by a covariant derivative, which is an operator that can differentiate sections of that bundle along tangent directions in the base manifold. Connections in this sense generalize, to arbitrary vector bundles, the concept of a linear connection on the tangent bundle of a smooth...
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In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure. Specifically, the similarity between a space E and a product space B × F is defined using a continuous surjective map
π
:
E
→
B
{\displaystyle \pi \colon E\to B}
that in small regions of E behaves just like a projection from corresponding regions of B × F to B. The map π, called the projection or submersion of the bundle, ...
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I am trying to study the moduli spaces of holomorphic vector bundles quickly, and I'm primarily interested in understanding:
Why and where the stability condition is used.
How are the moduli spaces constructed.
What are the examples, especially in the case of vector bundles on curves.
I was l...user228700
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I usually think of gravitational potential energy as representing just what it sounds like: the energy that we could potentially gain, using gravity. However, the equation for it (derived by integrating Newton's law of gravitational force)...
$PE_1 = -\frac{GMm}{r}$
..has me thrown for a loop...
Feynman Lectures. Lecture 43. Lecture Summary [http://www.feynmanlectures.caltech.edu/I_43.html]
$\text{The current of particles / area sec.} = - \frac{1}{3}lv\frac{dn_a}{dx} = - \mu kT\frac{dn_a}{dx} = - D\frac{d}{dx}(\frac{n_a}{n_0}).$
Can you show how did he get $\frac{n_a}{n_0}$ ? In ...
