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nLab > Latest Changes: differential cohomology

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  1.  
    • 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 𝒜\mathcal{A} a topological space

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

    the Hopkins-Singer differential cohomology with coefficients in 𝒜\mathcal{A} coincides with the differential cohomology with coefficients in AA in the (oo,1)-topos H\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

    added pointer to survey talk slides by Daniel Grady, here

    diff, v48, current

    • 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.

    diff, v54, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeSep 28th 2021

    Thanks for the pointer! I hadn’t know about this.

    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 CC-field in MM-theory is quantized using a differential refinement of Im(J)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

    Comments very welcome!

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeSep 28th 2021

    Yes, I was just sending them (hoping that makes sense) a comment (here) on the AT-dischord server

1 to 14 of 14

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