Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2015
    • (edited Nov 10th 2015)

    I have (finally) added some pointers to the result of Freed-Hopkins 13 to relevant nnLab 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 BG conn\mathbf{B}G_{conn} of principal connections (Freed-Hopkins 13):

    CE(𝔤) Ω licl (G) W(𝔤) Ω (EG conn) Ω (Ω(,𝔤)) inv(𝔤) Ω (BG conn) Ω (Ω(,𝔤)/G) \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) }