Traceless AF embeddings and unsuspended E-theory

Jamie Gabe (University of Glasgow)

Thursday 13th December, 2018 16:00-17:00 Maths 311B


A celebrated theorem of Kirchberg states that any separable, exact C*-algebra embeds into the Cuntz algebra O_2. In the same spirit, I have shown that a separable, exact C*-algebra embeds into the cone of O_2 if and only its primitive ideal space has no non-empty, compact, open subsets. Consequently, this characterises when traceless C*-algebras are AF embeddable, and (under nuclearity assumptions) when Connes and Higson's E-theory can be unsuspended. The latter result uses recent results of Dadarlat and Pennig.

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