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Introduction to Cyclic Cohomology
Masoud Khalkhali
University of Western Ontario
London, Ontario, Canada |
Abstract
Cyclic cohomology was discovered by Alain Connes in early 1980's. It
is the right noncommutative analogue of de Rham homology of currents on smooth manifolds. Since its inception, cyclic cohomology (and homology) have proved to be an indispensable tool in noncommutative geometry and its
applications. In this series of 12 lectures, we plan to cover most of what is known about cyclic cohomology and some of its applications. The lectures will be self contained and will start at a fairly basic level. Some familiarity with graduate level algebraic topology, functional analysis, and differential geometry will be useful. Topics will include:
1. Quantization of differential and integral calculus; cyclic
cocycles
2. Hochschild cohomology and homology; applications to
deformation theory
3. From cyclic cocycles to cyclic cohomology and homology
4. Where cyclic cocycles come from?
5. Chern-Connes character and
pairing with K-theory
6. Examples of computations of cyclic
cohomology: smooth manifolds,
group algebras,
noncommutative tori,
7. Applications
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| Time: | Aug. 12-17, 10:00-12:00
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| Place: | Lecture Hall, Niavaran Bldg., Niavaran Sqr., Tehran, Iran |
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