Timeline for Which bundles does the character variety parameterize?
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| Apr 27, 2016 at 13:17 | comment | added | Dmitry Vaintrob | You don't need to be careful about punctures unless you care about complex-analytical type data at the punctures. But (perhaps this is nitpicking), you do need to be careful about "instability". When $C$ is anything but a sphere with no punctures, the character variety parametrizes based maps $C\to BG$, i.e. principal $G$-bundles with chosen trivialization at the base point. (For $GL_n$, this is equivalent to vector bundles: in general, there is a standard dictionary, see en.wikipedia.org/wiki/Frame_bundle). When $C$ has $\pi_2 \neq 0$ with $G$ not discrete, the two may not be the same | |
| Sep 28, 2011 at 6:26 | history | answered | Sam Gunningham | CC BY-SA 3.0 |