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nLab > Latest Changes: twisted de Rham cohomology

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2020

    added pointer to the original article:

    diff, v6, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 31st 2020

    added pointer to

    diff, v7, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 31st 2020

    added pointer to:

    diff, v8, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 31st 2020

    added pointer to:

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 3rd 2020

    added pointer to:

    diff, v10, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 25th 2021

    added references for twists in degree 1 and for twists in degree higher than 3

    diff, v12, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 19th 2021

    am adding references (here) on 3-twisted de Rham cohomology generalized to equivariance/orbifolds

    diff, v13, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeAug 19th 2021

    started some lines on the definition of equivariant twisted de Rham cohomology according to Tu&Xu and others (here).

    It’s telegraphic for the moment, since first I wrote out some technical preliminaries (here) which made me run out of steam here.

    More later.

    diff, v15, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeAug 20th 2021

    I have added (here) some more lead-in words for the equivariant case (but still thin) and then I started to spell out (here) detail/proof for the claims implicit in FHT 07, (3.5).

    (What I don’t see yet is how to prove that the action of π 1\pi_1 on the cohomology of the fiber is trivial, so that their Serre spectral sequence really applies – have left a comment on this here.)

    diff, v17, current

    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTimeSep 28th 2021

    Added:

    A spectral sequence for twisted de Rham cohomology is discussed in

    • Weiping Li, Xiugui Liu, He Wang, On a spectral sequence for twisted cohomologies, arXiv:0911.1417.

    diff, v23, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 29th 2021

    Thanks. I have added publication data (here) and cross-linked with Atiyah&Segal05.

    diff, v24, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJan 9th 2022
    • (edited Jan 9th 2022)

    for when editing functionality is back:

    we should add pointer to

    • Pierre Deligne, Section II.6 in: Equations différentielles à points singuliers réguliers, Lecture Notes in Math 163, Springer 1970 (pdf, publication.ias:355)

    • Pavel I. Etingof, Igor Frenkel, Alexander A Kirillov, Section 7.2 in: Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations, Mathematical surveys and monographs 58, American Mathematical Society (1998)

    for textbook/moograph discussion of 1-twisted de Rham cohomology.

1 to 12 of 12

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