Abstract
We give a systematic account of the various pictures of -theory for real -algebras, proving natural isomorphisms between the groups that arise from each picture. As part of this project, we develop the universal properties of -theory, and we use CRT-structures to prove that a natural transformation between homotopy equivalent, stable, half-exact functors defined on real -algebras is an isomorphism, provided it is an isomorphism on the smaller class of -algebras. Finally, we develop -theory for real -algebras and use that to obtain new negative results regarding the problem of approximating almost commuting real matrices by exactly commuting real matrices.
Citation
Jeffrey L. Boersema. Terry A. Loring. Efren Ruiz. "Pictures of -theory for real -algebras and almost commuting matrices." Banach J. Math. Anal. 10 (1) 27 - 47, January 2016. https://doi.org/10.1215/17358787-3163312
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