 Browse by Category

Browse by School/
Graduate School
Ktheory for C*algebras, and beyond
Serge RICHARD Professor
Department: Graduate School of Mathematics
Class Time:  2015 Spring Friday 
Recommended for:  Graduate school of Mathematics 
Course Overview
Course Overview
This course will provide an overview of some recent tools introduced at the crossroad between functional analysis, geometry and operator algebras. It can be considered as a course on noncommutative topology, which is the first step toward noncommutative geometry. In order to provide a large panorama on the subject together with applications, some details might be omitted, but references for all proofs will be provided.
Close Section
Syllabus
Reference
There is no specific book related to this course. References and additional material will be provided during the lectures.
Plan of the course
Tentative program:
 C*algebras,
 Projections and unitaries,
 K_{0} and its properties,
 K_{1} and its properties,
 Index map and Bott periodicity,
 The sixterm exact sequence,
 Cyclic cohomology,
 Connes' pairing,
 Applications.
Keywords
C*algebras, Ktheory, index map, cyclic cohomology.
Required Knowledge
Knowledge on standard undergraduate functional analysis.
Attendance
This course is open for any students at Nagoya University as one of the “open subjects” of general education.
Additional advice
Lecture notes will be provided for this course.
Method of Evaluation
Grades based on attendance, written reports, and discussions.
Close Section
Class Materials
Lecture Notes
 First lecture
 Introduction (PDF, 40KB)
 full document (110 pages)
 Ktheory for C*algebras, and beyond (PDF, 453KB)
Lecture Notes
 Title (PDF, 33KB)
 Contents (PDF, 58KB)
 Chapter 1
 C*algebras (PDF, 132KB)
 Chapter 2
 Projections and unitary elements (PDF, 135KB)
 Chapter 3
 K_0group for a unital C*algebra (PDF, 132KB)
 Chapter 4
 K_0group for an arbitrary C*algebra (PDF, 110KB)
 Chapter 5
 The functor K_1 (PDF, 108KB)
 Chapter 6
 The index map (PDF, 112KB)
 Chapter 7
 Higher Kfunctors, Bott periodicity (PDF, 129KB)
 Chapter 8
 The sixterm exact sequence (PDF, 93KB)
 Chapter 9
 Cyclic cohomology (PDF, 193KB)
 Chapter 10
 Application: Levinson's theorem (PDF, 128KB)
 Bibliography
 Bibliography (PDF, 51KB)
Close Section
Page last updated August 7, 2015
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.