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

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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).

nLab > Latest Changes: nonabelian cohomology

Bottom of Page

1 to 14 of 14

  1.  

  1. I added a reference to a paper of mine

    Amnon Yekutieli

    diff, v48, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 15th 2020

    added pointer to

    • Jinpeng An. Zhengdong Wang, Nonabelian cohomology with coefficients in Lie groups,Trans. Amer. Math. Soc. 360 (2008), 3019-3040 (doi:10.1090/S0002-9947-08-04278-5)

    diff, v51, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 15th 2020

    added these pointers:

    diff, v51, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 15th 2020

    added pointer to

    diff, v51, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 15th 2020
    • (edited Aug 15th 2020)

    For citation purposes, what’s a good (textbook) account that makes explicit both the concept of non-abelian cohomology and its representation by classifying spaces (under suitable conditions)

    I am asking, because the literature on “non-abelian cohomology” tends to jump to arcane properties before ever saying clearly what the (simple) main structure of the general theory actually is. As a result, it is hard to tell a reader “see reference XYZ”, because if they don’t already know about the topic, they might not even recognize that XYZ is about this topic.

    The article Roberts-Stevenson 12 above stands out in this respect, as it does state these general principle on the first three pages, even if not quite in an expository way.

    But ignoring higher groups and stuff, just focusing on the ancient theory. What’s your preferred textbook(-style) reference that makes clear that non-abelian cohomology is a thing and that its ultimately about maps into classifying spaces?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 15th 2020

    I have tried to give some more logical order to the list of references.

    Now I have introduced 3 subsections under “References”, correspondoing to discussion in homotopical dimensioon 1, 2, ∞\infty, respectively.

    diff, v52, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 18th 2020

    added pointer to

    diff, v54, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2020
    • (edited Sep 2nd 2020)

    added pointer to

    diff, v57, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2020

    added pointer to

    diff, v57, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2020

    added publication data to:

    diff, v58, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 11th 2020

    added publication details to:

    • Carlos Simpson, Algebraic aspects of higher nonabelian Hodge theory, in: Fedor Bogomolov, Ludmil Katzarkov (eds.), Motives, polylogarithms and Hodge theory, Part II (Irvine, CA, 1998), Int. Press Lect. Ser., 3, II, Int. Press, 2002, 2016, 417-604. (arXiv:math/9902067, ISBN:9781571462909)

    diff, v59, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJan 19th 2021
    • (edited Jan 19th 2021)

    added pointer to

    (since unstable operations on stable cohomology is really operations on their image in non-abelian cohomology)

    diff, v61, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeJul 14th 2021

    added pointer to:

    diff, v64, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2021

    added pointer to:

    diff, v65, current

1 to 14 of 14

  1.