Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor 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 nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics 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

1. • CommentRowNumber1.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 27th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI have a vague memory that someone in the higher geometry crew once mentioned this in a more or less formal setting (a paper or talk, but maybe only here). Namely the geometric objects classified by $\mathbf{B}(\mathbf{B}^2U(1)_{conn})$. Unfortunately the only explicit mention I can find is (2.2) in _[The WZW term of the M5-brane and differential cohomotopy](https://arxiv.org/abs/1506.07557)_, and it's not what I was thinking of. This should be something like bundle 2-gerbes with connection and curving, but where the trivialisation on triple overlaps is as a bundle gerbe **with connection**. This is stronger than is usually specified in the literature, and I needed to point to a place where this is discussed, if at all. If such a discussion doesn't exist, then that's totally ok, I just wanted to check my memory wasn't tricking me.

   I have a vague memory that someone in the higher geometry crew once mentioned this in a more or less formal setting (a paper or talk, but maybe only here). Namely the geometric objects classified by $\mathbf{B}(\mathbf{B}^2U(1)_{conn})$. Unfortunately the only explicit mention I can find is (2.2) in The WZW term of the M5-brane and differential cohomotopy, and it’s not what I was thinking of.

   This should be something like bundle 2-gerbes with connection and curving, but where the trivialisation on triple overlaps is as a bundle gerbe with connection. This is stronger than is usually specified in the literature, and I needed to point to a place where this is discussed, if at all. If such a discussion doesn’t exist, then that’s totally ok, I just wanted to check my memory wasn’t tricking me.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 27th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexAs a step in the "Hodge filtration" of the Deligne complex this gadget appears as Prop. 1.3 in the talk notes [here](https://ncatlab.org/schreiber/files/DiffCoIsCoHo.pdf), which eventually evolved into Section 5.2.13.4 in dcct "v2", starting [p. 470 here](https://ncatlab.org/schreiber/files/dcct170811.pdf#page=497). In the example of the delooped canonical *multiplicative* bundle gerbe it appears on [p. 40 here](https://arxiv.org/pdf/1304.0236.pdf#page=40) and in an analogous form down in the degree you may be expecting on [p. 46](https://arxiv.org/pdf/1304.0236.pdf#page=46)).

   As a step in the “Hodge filtration” of the Deligne complex this gadget appears as Prop. 1.3 in the talk notes here, which eventually evolved into Section 5.2.13.4 in dcct “v2”, starting p. 470 here.

   In the example of the delooped canonical multiplicative bundle gerbe it appears on p. 40 here and in an analogous form down in the degree you may be expecting on p. 46).

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 27th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexHmm, Ok. I'm going to do a little dig through Konrad's papers, if he doesn't offer an answer here, but I might have just invented something or confused what I'd read with something else. Thanks, though!

   Hmm, Ok. I’m going to do a little dig through Konrad’s papers, if he doesn’t offer an answer here, but I might have just invented something or confused what I’d read with something else. Thanks, though!

4. • CommentRowNumber4.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMay 27th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexThis type of object is where the off-diagonal characteristic classes live. See Chapter 16 in Amabel–Debray–Haine. By the way, does the nLab has anything about off-diagonal characteristic classes in differential cohomology?

   This type of object is where the off-diagonal characteristic classes live. See Chapter 16 in Amabel–Debray–Haine.

   By the way, does the nLab has anything about off-diagonal characteristic classes in differential cohomology?

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 27th 2022
   • (edited May 27th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexas far as I remember, these truncated Deligne complexes appear on the nLab, so far, only [here](https://ncatlab.org/nlab/show/intermediate+Jacobian#CharacterizationAsHodgeTrivialDeligneCohomology) in the entry on [[intermediate Jacobians]]

   as far as I remember, these truncated Deligne complexes appear on the nLab, so far, only here in the entry on intermediate Jacobians