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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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.
   • CommentAuthorUrs
   • CommentTimeJul 29th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexOn my personal web, I am working on a page titled <a href="http://ncatlab.org/schreiber/show/differential+cohomology+in+an+(%E2%88%9E%2C1)-topos+--+examples">differential cohomology in an (oo,1)-topos -- Examples</a>. So far, I have been spelling out <a href="http://ncatlab.org/schreiber/show/differential+cohomology+in+an+(%E2%88%9E%2C1)-topos+--+examples#AbGerbe">here</a> in some detail how the ordinary notion of [[Deligne cohomology]]/[[Cheeger-Simons differential character]]s aka "bundle $n$-gerbes with connection" drops out from the abstract $(\infty,1)$-topos-theoretic definition of differential cohomology, applied to the topos of [[Lie-infinity groupoid]]s. Specifically, I have been focusing on an <a href="http://ncatlab.org/schreiber/show/differential+cohomology+in+an+(%E2%88%9E%2C1)-topos+--+examples#CircleBundlesConnection">expositional section</a> that discusses just the case of ordinary $U(1)$-principal bundles with connection in this light. Eventually I am hoping to find some $\beta$-testers of these writeups. Maybe it's at too early a stage, since I need to polish various things. But since I have to run now and do something else, I thought: why not drop a mentioning of this on the $n$Forum?

   On my personal web, I am working on a page titled differential cohomology in an (oo,1)-topos – Examples.

   So far, I have been spelling out here in some detail how the ordinary notion of Deligne cohomology/Cheeger-Simons differential characters aka “bundle $n$-gerbes with connection” drops out from the abstract $(\infty,1)$-topos-theoretic definition of differential cohomology, applied to the topos of Lie-infinity groupoids.

   Specifically, I have been focusing on an expositional section that discusses just the case of ordinary $U(1)$-principal bundles with connection in this light.

   Eventually I am hoping to find some $\beta$-testers of these writeups. Maybe it’s at too early a stage, since I need to polish various things. But since I have to run now and do something else, I thought: why not drop a mentioning of this on the $n$Forum?