Atiyah-Bott-Shapiro for graded, Real C*-algebrasOberseminar Global Analysis and Operator Algebras

by Anupam Datta (MI (Uni Bonn))

Tuesday May 12, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

Classically, Atiyah-Bott-Shapiro (ABS) describe (Real) K-groups of a point in terms of certain Clifford module quotients. It is plausible to ask what happens for a general graded, Real C*-algebra. We show that a version of the ABS isomorphism can be recovered in a homotopy theoretic sense : there will be a long exact sequence connecting graded and ungraded K-theories. We deduce this as a consequence of recent higher categorical developments in KK-theory a' la Bunke. In the process, we clarify and generalise certain results of Ulrich Haag on graded KK-theory. This is work in progress.