started something at *splitting principle*

(wanted to do more, but need to interrupt now)

]]>at *field (physics)* I needed to point to something with “electroweak” in its title. So I created a brief entry *electroweak field*.

Somehow I was under the impression that I had written out on the $n$Lab at several places how the traditional physics way to talk about instantons connects to the correct maths discussion. But now that I wanted to point a physicist to this, I realize that in each entry that touches on this, I just gave a quick remark pointing to Cech cohomology, clutching construction, one-point compactification and Chern-Simons 2-gerbes, but not actually giving an exposition.

So I went ahead and wrote such an exposition finally:

*SU2-instantons from the correct maths to the traditional physics story*

Beware two things:

1) this entry is meant to be included as a subsection into other entries (such as Yang-Mills instanton, BPTS instanton) therefore it is intentionally lacking toc, headlines and other introductory stuff

2) I just wrote this in one go (trying to get back to somebody waiting for me), and now I am out of steam. This hasn’t been proof-read even once yet. So unless you feel energetic about joining in the editing, better wait until a little later when this has stabilized.

Ideally this kind of account would eventually be beautified with some pictures and the like.

]]>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):

$\array{ CE(\mathfrak{g}) &\simeq& \Omega^\bullet_{li \atop cl}(G) \\ \uparrow && \uparrow \\ W(\mathfrak{g}) &\simeq & \Omega^\bullet(\mathbf{E}G_{conn}) & \simeq & \Omega^\bullet(\mathbf{\Omega}(-,\mathfrak{g})) \\ \uparrow && \uparrow \\ inv(\mathfrak{g}) &\simeq& \Omega^\bullet(\mathbf{B}G_{conn}) & \simeq & \Omega^\bullet(\mathbf{\Omega}(-,\mathfrak{g})/G) }$ ]]>started some minimum at *odd Chern character* and cross-linked a little

started some minimum at *Donaldson-Uhlenbeck-Yau theorem*

When I was about to create it for *flat connection* I notice that we already did have *Riemann-Hilbert correspondence*. So now I have cross-linked it with *flat connection*, *flat infinity-connection*, *local system*, *Riemann-Hilbert problem* and the latter with *Hilbert’s problems*

created a table

*infinity-CS theory for binary non-degenerate invariant polynomial - table*

adapted from

- Pavol Ševera,
*Some title containing the words “homotopy” and “symplectic”, e.g. this one*

and included it into the relevant entries

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