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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 29th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexthis page needs attention. For the moment I have at least added these original articles: * [[Michael Atiyah]], [[Isadore Singer]], *Index theory for skew-adjoint Fredholm operators*, Publications Mathématiques de l'IHÉS, Tome **37** (1969) 5-26 $[$[numdam:PMIHES_1969__37__5_0](http://www.numdam.org/item/PMIHES_1969__37__5_0)$]$ * [[Max Karoubi]], *Espaces Classifiants en K-Théorie*, Transactions of the American Mathematical Society **147** 1 (Jan., 1970) 75-115 $[$[doi:10.2307/1995218](https://doi.org/10.2307/1995218)$]$ <a href="https://ncatlab.org/nlab/revision/diff/Karoubi+K-theory/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/Karoubi+K-theory/10">v10</a>, <a href="https://ncatlab.org/nlab/show/Karoubi+K-theory">current</a>

   this page needs attention. For the moment I have at least added these original articles:

   • Michael Atiyah, Isadore Singer, Index theory for skew-adjoint Fredholm operators, Publications Mathématiques de l’IHÉS, Tome 37 (1969) 5-26 $[$numdam:PMIHES_1969__37__5_0$]$

   • Max Karoubi, Espaces Classifiants en K-Théorie, Transactions of the American Mathematical Society 147 1 (Jan., 1970) 75-115 $[$doi:10.2307/1995218$]$

   diff, v10, current

2. • CommentRowNumber2.
   • CommentAuthorperezl.alonso
   • CommentTimeMay 25th 2024
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexpointer * [[Max Karoubi]], _K-theory: An introduction_. Springer Science & Business Media, 2009. ([doi](https://doi.org/10.1007/978-3-540-79890-3)). <a href="https://ncatlab.org/nlab/revision/diff/Karoubi+K-theory/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/Karoubi+K-theory/12">v12</a>, <a href="https://ncatlab.org/nlab/show/Karoubi+K-theory">current</a>

   pointer

   • Max Karoubi, K-theory: An introduction. Springer Science & Business Media, 2009. (doi).

   diff, v12, current

3. • CommentRowNumber3.
   • CommentAuthorLuuk
   • CommentTime5 days ago
   • PermaLink
   Author: Luuk
   Format: TextThis page is misleading: it is not true in the Karoubi model that Kn(x) is Cln-module bundles on X modulo those that extend to a Cln+1-module bundle. Such a description would imply K^1(S^1) = 0. Karoubi triples are slightly more subtle than an Atyah-Bott-Shapiro style definition of K-theory.

   This page is misleading: it is not true in the Karoubi model that Kn(x) is Cln-module bundles on X modulo those that extend to a Cln+1-module bundle. Such a description would imply K^1(S^1) = 0. Karoubi triples are slightly more subtle than an Atyah-Bott-Shapiro style definition of K-theory.
4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTime5 days ago
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added the actual definition, with pointers to [Karoubi 1978](https://ncatlab.org/nlab/show/Karoubi+K-theory#Karoubi78), and adjusted the previous wording a little. (The original text was taken from [here](https://golem.ph.utexas.edu/category/2007/10/higher_clifford_algebras.html#c012972)). <a href="https://ncatlab.org/nlab/revision/diff/Karoubi+K-theory/13">diff</a>, <a href="https://ncatlab.org/nlab/revision/Karoubi+K-theory/13">v13</a>, <a href="https://ncatlab.org/nlab/show/Karoubi+K-theory">current</a>

   I have added the actual definition, with pointers to Karoubi 1978,

   and adjusted the previous wording a little. (The original text was taken from here).

   diff, v13, current