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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 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 topological topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 30th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexI was about to create a new entry "characteristic differential form" when I discrovered this old entry. Have added more redirects to it and more cross-links with _[[Chern-Weil homomorphism]]_. <a href="https://ncatlab.org/nlab/revision/diff/curvature+characteristic+form/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/curvature+characteristic+form/8">v8</a>, <a href="https://ncatlab.org/nlab/show/curvature+characteristic+form">current</a>

   I was about to create a new entry “characteristic differential form” when I discrovered this old entry.

   Have added more redirects to it and more cross-links with Chern-Weil homomorphism.

   diff, v8, current

2. • CommentRowNumber2.
   • CommentAuthorDean
   • CommentTimeMay 15th 2025
   • (edited May 15th 2025)
   • PermaLink
   Author: Dean
   Format: MarkdownItexCan someone help me with (4) in the section "Preliminaries"? I think one of the $\Omega^{2}$'s should be $\Omega^{2 \cdot}$. (Also, $\Omega^{2}$ is not a ring or algebra on its own.)

   Can someone help me with (4) in the section “Preliminaries”?

   I think one of the ’s should be . (Also, is not a ring or algebra on its own.)

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 16th 2025
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe powers of $\Omega$ in (4) look correct to me: The formula is including a 2-form into the ring if even-degree forms. But the variable "$t$" is either missing in the last term or spurious in the second-but-last. I am deleting it now.

   The powers of in (4) look correct to me: The formula is including a 2-form into the ring if even-degree forms.

   But the variable “” is either missing in the last term or spurious in the second-but-last. I am deleting it now.