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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 20th 2010

I am (slowly) working on bringing the entry differential cohomology in better shape.

For the moment I am adding a section on the Hopkins-Singer formulation.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeApr 21st 2010

I see Ulrich's influence :) Don't forget to learn something about eta invariants and determinant line bundles (in the business of zeta function renormalization and quantum anomalies), he has a number of papers on them (I do not know what was his motivation).

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeApr 21st 2010

That’s a good suggestion, Zoran, but I am afraid there is no time for that. But I’ll see.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 21st 2010
• (edited Apr 21st 2010)

I added a (very brief so far) Properties-section on the Hopkins-Singer definition.

Then I wrote on my personal web in the section General differential cohomology the outline of an argument that is supposed to show that

• for $\mathcal{A}$ a topological space

• and $A = LConst Sing \mathcal{A}$ its incarnation as a constant oo-stack in $\mathbf{H} = Sh_{\infty}(CartSp)$,

the Hopkins-Singer differential cohomology with coefficients in $\mathcal{A}$ coincides with the differential cohomology with coefficients in $A$ in the (oo,1)-topos $\mathbf{H}$, as defined there.

Needs more attention, but I have to run now to get some breakfast…

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeApr 25th 2014

I am finally getting to brushing-up the entry on differential cohomology (which has been – of all entries! – woefully neglected).

For the moment I have polished and considerably expanded the Idea section and brushed-up and commented the list of references.

In particular I am splitting off an entry differential cohomology hexagon.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeApr 24th 2018

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeSep 16th 2020

I have added references, but upon saving and now upon viewing the entry, it throws the following error message:

  XML Parsing Error: mismatched tag. Expected: </div>.
Location: https://ncatlab.org/nlab/show/differential+cohomology
Line Number 545, Column 3:
</ul>
--^


Apparently this is caused by some code that was there before, which got re-saved now with a stricter parser. But I haven’t found the problematic line yet…

• CommentRowNumber8.
• CommentAuthorRichard Williamson
• CommentTimeSep 16th 2020
• (edited Sep 16th 2020)

I have fixed it now. The problem came from the table of contents rendering; the problem was the use of a customised theorem name in the theorems attributed to Hopkins-Singer and Bunke-Schick, which caused the renderer to think that these theorems were sections. Unnumbered theorem environments were also being used. I have now changed the environments to numbered ones, and added the attributions to Hopkins-Singer and Bunke-Schick in a slightly different way which does not break things.

• CommentRowNumber9.
• CommentAuthorUlrik
• CommentTimeSep 28th 2021

Add the new book edited by Amabel, Debray, and Haine.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeSep 28th 2021

Let’s add the author-entries you are requesting. Will do now…

• CommentRowNumber11.
• CommentAuthorDavid_Corfield
• CommentTimeSep 28th 2021
• (edited Sep 28th 2021)

there is also the ambitious “hypothesis H” of Fiorenza–Sati–Schreiber [Sat18; FSS19; FSS20b] proposing that the $C$-field in $M$-theory is quantized using a differential refinement of $Im(J)$-twisted stable cohomotopy instead.

Doesn’t need that ’stable’.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeSep 28th 2021
• (edited Sep 28th 2021)

True.

Speaking of which, I am taking the liberty of adding (here) pointer to Section 4.3 in

where differential cohomology via $\infty$-sheaves is set up in the non-abelian generality that accomodates differential refinements of un-stable Cohomotopy theory.

• CommentRowNumber13.
• CommentAuthorDavid_Corfield
• CommentTimeSep 28th 2021

The arxiv page says