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arXiv · 1210.3133

Pictures of KK-theory for real C*-algebras and almost commuting matrices

Jeffrey L. Boersema·Terry A. Loring·Efren Ruiz
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Abstract

We give a systematic account of the various pictures of KK-theory for real C*-algebras, proving natural isomorphisms between the groups that arise from each picture. As part of this project, we develop the universal properties of KK-theory, and we use CRT-structures to prove that a natural transformation from F(A) to G(A) between homotopy equivalent, stable, half-exact functors defined on real C*-algebras is an isomorphism provided it is an isomorphism on the smaller class of C*-algebras. Finally, we develop E-theory for real C*-algebras and use that to obtain new negative results regarding the problem of approximating almost commuting real matrices by exactly commuting real matrices.

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Jeffrey L. Boersema, Terry A. Loring, Efren Ruiz. 2012-10-11. Pictures of KK-theory for real C*-algebras and almost commuting matrices. https://doi.org/10.1215/17358787-3163312

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