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From the Basic Homotopy Lemma to the Classification of $C^*$-algebras

Huaxin Lin East China Normal University, Shanghai, China and University of Oregon, Eugene, OR
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-1-4704-3490-8
Product Code: CBMS/124
List Price: $52.00 MAA Member Price:$46.80
AMS Member Price: $41.60 Electronic ISBN: 978-1-4704-4192-0 Product Code: CBMS/124.E List Price:$52.00
MAA Member Price: $46.80 AMS Member Price:$41.60
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List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Click above image for expanded view From the Basic Homotopy Lemma to the Classification of$C^*$-algebras Huaxin Lin East China Normal University, Shanghai, China and University of Oregon, Eugene, OR A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-1-4704-3490-8 Product Code: CBMS/124  List Price:$52.00 MAA Member Price: $46.80 AMS Member Price:$41.60
 Electronic ISBN: 978-1-4704-4192-0 Product Code: CBMS/124.E
 List Price: $52.00 MAA Member Price:$46.80 AMS Member Price: $41.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1242017; 240 pp
MSC: Primary 46;

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 $C^*$-algebras, 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.

A co-publication of the AMS and CBMS.

Graduate students and researchers interested in C*-algebras.

• Chapters
• An overview of the Elliott program
• An introduction to the Basic Homotopy Lemma
• Maps to finite dimensional $C^*$-algebras
• Stable homotopy lemmas
• The Basic Homotopy Lemma, finite dimensional cases
• $C^*$-algebras of generalized tracial rank one
• More Basic Homotopy Lemmas
• Asymptotic unitary equivalence
• Classification of simple $C^*$-algebras of finite rank

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 1242017; 240 pp
MSC: Primary 46;

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 $C^*$-algebras, 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.

A co-publication of the AMS and CBMS.

Graduate students and researchers interested in C*-algebras.

• Chapters
• An overview of the Elliott program
• An introduction to the Basic Homotopy Lemma
• Maps to finite dimensional $C^*$-algebras
• Stable homotopy lemmas
• The Basic Homotopy Lemma, finite dimensional cases
• $C^*$-algebras of generalized tracial rank one
• More Basic Homotopy Lemmas
• Asymptotic unitary equivalence
• Classification of simple $C^*$-algebras of finite rank
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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