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
   • CommentTimeOct 4th 2020
   • (edited Oct 4th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something <a href="https://ncatlab.org/nlab/revision/equivariant+Chern-Dold+character/1">v1</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern-Dold+character">current</a>

   starting something

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 4th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am expecting that the equivariant Chern character in equivariant K-theory is naturally induced by the [[equivariant rationalization]]-map on the classifying $G$-space for equivaraiant K-theory. Instead, people like to give various fairly involved component-definitions of the equivariant Chern character. That these component definitions are indeed equivalent to the natural definition by rationalization of the classifying $G$-space appears, as a side remark, below the proof of Theorem 5.5 in [Lück-Oliver 01](https://ncatlab.org/nlab/show/equivariant+Chern+character#LueckOliver01). Does any author make this more explicit?

   I am expecting that the equivariant Chern character in equivariant K-theory is naturally induced by the equivariant rationalization-map on the classifying $G$-space for equivaraiant K-theory.

   Instead, people like to give various fairly involved component-definitions of the equivariant Chern character.

   That these component definitions are indeed equivalent to the natural definition by rationalization of the classifying $G$-space appears, as a side remark, below the proof of Theorem 5.5 in Lück-Oliver 01.

   Does any author make this more explicit?