The spectral model of (Real) $K$-theory

Abstract

We use homotopy theoretic ideas to study the $K$-theory of (graded, Real) $C^{\ast }$-algebras in detail. After laying the foundations, and deriving the formal properties, the comparison of the model with the Kasparov picture of $K$-theory has been made, and Bott periodicity has been proven using a Dirac-dual Dirac method.

This article is roughly the content of the author's masters thesis written under the supervision of Prof. Dr. Johannes Ebert at the University of Muenster in 2023. An updated version will be available at a later date