From the basic homotopy lemma to the classification of C*-algebras - number 124

This book examines some recent developments in the theory of $C^*$-algebras, which are algebras of operators on Hilbert spaces.

An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries.

The book presents an outline of the background as well as some recent results of the classification of simple amenable $C^*$-algebra, otherwise known as the Elliott program.

This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy.

Furthermore, $KK$-theory related rotation maps are introduced.

The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.