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Results tagged with chern-classes
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user 120604
Characteristic classes associated to complex vector bundles.
8
votes
0
answers
547
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What is $SL(2,\mathbb{R})$-Chern-SImons Theory?
I found in physics that Chern-Simons theory is closely related with three dimensional gravity.
From this paper Three Dimensional Gravity Revisited, the author talks about the Chern-Simons for
$$\m …
- 615
1
vote
1
answer
255
views
Why is the Chern Number Invariant under A Continuously Shrinking of the Structure Group?
In Witten's paper Three Dimensional Gravity Revisited and Quantization of Chern-Simons Theory with Complex Gauge Group, he used a fact that for a principal $G$-bundle, the quantization of the Chern nu …
- 615
4
votes
0
answers
853
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When is the Chern class of a principal $G$-bundle same to the Chern class of the associated ...
Let $P\rightarrow M$ be a principal bundle, with structure group $G$. If $G$ has a representation $\rho:G\rightarrow GL(n,\mathbb{C})$, then we can define its associated vector bundle $E=P\times_{\rho …
- 615
5
votes
1
answer
264
views
The existence of the extension of a non-trivial line bundle
In Three Dimensional Gravity Revisted, Witten studied the Abelian Chern-Simons theory in three dimensions.
Let $W$ be a three dimensional manifold. Let $\mathcal{L}$ be a non-trivial line-bundle over …
- 615