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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 20th 2017
   • (edited Jul 20th 2017)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI added to [[transchromatic character]] * [[Nathaniel Stapleton]], _An Introduction to HKR Character Theory_ ([pdf](http://homepages.uni-regensburg.de/~stn30788/papers/Characters.pdf)) and * [[Takeshi Torii]], _HKR characters, p-divisible groups and the generalized Chern character_, ([pdf](http://www.ams.org/journals/tran/2010-362-11/S0002-9947-2010-05194-3/S0002-9947-2010-05194-3.pdf))

   I added to transchromatic character

   • Nathaniel Stapleton, An Introduction to HKR Character Theory (pdf)

   and

   • Takeshi Torii, HKR characters, p-divisible groups and the generalized Chern character, (pdf)
2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 21st 2017
   • (edited Jul 21st 2017)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThe most accessible account for me that I've found on why a transchromatic character is a generalisation of an ordinary character is in the first 7 pages of an undergraduate thesis, albeit one supervised by Lurie: * Arpon Raksit, _Characters in global equivariant cohomology theory_, [pdf](http://www.math.harvard.edu/theses/senior/raksit/raksit.pdf) Probably not what we'd normally use. Anyway, I'll copy over the idea there of [[group characters]] as the zero-th cohomology of $Map(S^1,B G)$.

   The most accessible account for me that I’ve found on why a transchromatic character is a generalisation of an ordinary character is in the first 7 pages of an undergraduate thesis, albeit one supervised by Lurie:

   • Arpon Raksit, Characters in global equivariant cohomology theory, pdf

   Probably not what we’d normally use. Anyway, I’ll copy over the idea there of group characters as the zero-th cohomology of $Map(S^1,B G)$.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 10th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to [Raksit 15](https://ncatlab.org/nlab/show/transchromatic+character#Raksit15) <a href="https://ncatlab.org/nlab/revision/diff/transchromatic+character/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/transchromatic+character/9">v9</a>, <a href="https://ncatlab.org/nlab/show/transchromatic+character">current</a>

   added pointer to Raksit 15

   diff, v9, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeOct 10th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexoh, we overlapped, I was just adding this

   oh, we overlapped, I was just adding this

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeOct 10th 2018
   • (edited Oct 10th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItex[ wrong thread ]

   [ wrong thread ]

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeNov 8th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data to: * [[Nathaniel Stapleton]], _Transchromatic twisted character maps_, J. Homotopy Relat. Struct. 10, 29–61 (2015). ([arXiv:1304.5194](https://arxiv.org/abs/1304.5194), [doi:10.1007/s40062-013-0040-9](https://doi.org/10.1007/s40062-013-0040-9)) <a href="https://ncatlab.org/nlab/revision/diff/transchromatic+character/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/transchromatic+character/11">v11</a>, <a href="https://ncatlab.org/nlab/show/transchromatic+character">current</a>

   added publication data to:

   • Nathaniel Stapleton, Transchromatic twisted character maps, J. Homotopy Relat. Struct. 10, 29–61 (2015). (arXiv:1304.5194, doi:10.1007/s40062-013-0040-9)

   diff, v11, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJul 3rd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have cross-linked with *[[Huan's inertia orbifold]]*. It's at the bottom of [p. 2](https://arxiv.org/pdf/1304.5194.pdf#page=2) of [arXiv:1304.5194](https://arxiv.org/abs/1304.5194) that Stapleton almost writes down Huan's inertia model. The place where this thought is picked up seems to be Remark 4.9 on [p. 20](https://arxiv.org/pdf/1304.5194.pdf#page=20). I still need to digest Stapleton's notation more fully, but what that remark indicates is probably the co-free 2-action that I worked out [here](https://ncatlab.org/nlab/show/Borel+model+structure#BZActionOnInertiaGroupoid). <a href="https://ncatlab.org/nlab/revision/diff/transchromatic+character/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/transchromatic+character/14">v14</a>, <a href="https://ncatlab.org/nlab/show/transchromatic+character">current</a>

   I have cross-linked with Huan’s inertia orbifold.

   It’s at the bottom of p. 2 of arXiv:1304.5194 that Stapleton almost writes down Huan’s inertia model. The place where this thought is picked up seems to be Remark 4.9 on p. 20. I still need to digest Stapleton’s notation more fully, but what that remark indicates is probably the co-free 2-action that I worked out here.

   diff, v14, current