From the Basic Homotopy Lemma to the Classification of $C^*$-algebras (CBMS Regional Conference Series in Mathematics). Este artículo no está disponible.From the Basic Homotopy Lemma to the Classification of $C^*$-algebras (CBMS Regional Conference Series in Mathematics)

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.

Huaxin Lin, East China Normal University, Shanghai, China, and University of Oregon, Eugene, OR.