Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
1 to 1 of 1
I have (finally) added some pointers to the result of Freed-Hopkins 13 to relevant $n$Lab entries.
Mostly at Weil algebra – characterization in the smooth infinity-topos
also at invariant polynomials – As differential forms on the moduli stack of connections
pointing out that this adds further rationalization to the construction of connections on principal infinity-bundles – via Lie integration.
In making these edits, I have created and then used a little table-for-inclusion
Presently this displays as follows:
Chevalley-Eilenberg algebra CE $\leftarrow$ Weil algebra W $\leftarrow$ invariant polynomials inv
differential forms on moduli stack $\mathbf{B}G_{conn}$ of principal connections (Freed-Hopkins 13):
$\array{ CE(\mathfrak{g}) &\simeq& \Omega^\bullet_{li \atop cl}(G) \\ \uparrow && \uparrow \\ W(\mathfrak{g}) &\simeq & \Omega^\bullet(\mathbf{E}G_{conn}) & \simeq & \Omega^\bullet(\mathbf{\Omega}(-,\mathfrak{g})) \\ \uparrow && \uparrow \\ inv(\mathfrak{g}) &\simeq& \Omega^\bullet(\mathbf{B}G_{conn}) & \simeq & \Omega^\bullet(\mathbf{\Omega}(-,\mathfrak{g})/G) }$1 to 1 of 1