Timeline for Why is Lie's Third Theorem difficult?
Current License: CC BY-SA 2.5
6 events
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| Nov 20, 2015 at 10:38 | comment | added | Alexander Alldridge | This point of view is essentially the one followed by Duistermaat and Kolk in their book on Lie groups (Springer Universitext 2004), see Theorem 1.14.3 there. In fact, $\tilde G$ is constructed as a quotient of the path space of $\mathfrak g$. The point at which the vanishing of $\pi_2(G)$ enters is somewhat subtle. Duistermaat and Kolk use that $H^2(G,\mathbb R)=0$ for a simply connected Lie group. This is applied to the universal covering of the adjoint group of $\mathfrak g$. This eventually implies the Hausdorff property of the leaf space (or, equivalently, the quotient of the path space). | |
| Feb 28, 2011 at 4:34 | comment | added | Eric Wofsey | Can you say more about how $\pi_2$ relates to patching together copies of the neighborhood of the origin given by BCH? Can you, say, give a simple explicit construction of an obstruction to this patching that lives in $\pi_2$? | |
| Feb 27, 2011 at 18:18 | history | edited | Ezra Getzler | CC BY-SA 2.5 |
Added definition of infinitesimal gauge transformation; deleted 15 characters in body
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| Feb 24, 2011 at 12:52 | comment | added | Theo Johnson-Freyd | Awesome. And welcome to MathOverflow! | |
| Feb 24, 2011 at 12:31 | comment | added | AFK | Could you please explain what "the foliation of the space of g-connections on the 1-simplex associated to infinitesimal gauge transformation" is? | |
| Feb 24, 2011 at 7:30 | history | answered | Ezra Getzler | CC BY-SA 2.5 |