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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 18th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexa bare minimum, for the moment just to have a place for recording references <a href="https://ncatlab.org/nlab/revision/twisted+equivariant+Chern+character/1">v1</a>, <a href="https://ncatlab.org/nlab/show/twisted+equivariant+Chern+character">current</a>

   a bare minimum, for the moment just to have a place for recording references

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 19th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexQuestion: Taken at face value, the codomain of the twisted equivaraint Chern character according to [Mathai & Stevenson 2003](https://ncatlab.org/nlab/show/twisted+equivariant+Chern+character#MathaiStevenson03) looks different from that of (all ?) other authors: * The former take it to be the Weil-model equivariant de Rham complex twisted by a closed degree-3 element in the evident way, * the other authors consider flat-line bundle-twisted de Rham cohomology on the inertia orbifold further twisted by the 3-form. Probably these two codomains are quasi-isomorphic? But it doesn't seem to be obvious. Is this discussed anywhere?

   Question:

   Taken at face value, the codomain of the twisted equivaraint Chern character according to Mathai & Stevenson 2003 looks different from that of (all ?) other authors:

   • The former take it to be the Weil-model equivariant de Rham complex twisted by a closed degree-3 element in the evident way,

   • the other authors consider flat-line bundle-twisted de Rham cohomology on the inertia orbifold further twisted by the 3-form.

   Probably these two codomains are quasi-isomorphic? But it doesn’t seem to be obvious. Is this discussed anywhere?