Homological Methods in Noncommutative Geometry
by D. Kaledin
Number of pages: 77
The first seven lectures deal with the homological part of the story (cyclic homology, its various definitions, various additional structures it possesses). Then there are four lectures centered around Hochschild cohomology and the formality theorem.
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by Masoud Khalkhali - University of Western Ontario
Contents: Introduction; Some examples of geometry-algebra correspondence; Noncommutative quotients; Cyclic cohomology; Chern-Connes character; Banach and C*-algebras; Idempotents and finite projective modules; Equivalence of categories.
by Alain Connes - Academic Press
The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.
by Travis Schedler - arXiv
In these notes, we give an example-motivated review of the deformation theory of associative algebras in terms of the Hochschild cochain complex as well as quantization of Poisson structures, and Kontsevich's formality theorem in the smooth setting.
by Thierry Masson - arXiv
This is an extended version of a three hours lecture given at the 6th Peyresq meeting 'Integrable systems and quantum field theory'. We make an overview of some of the mathematical results which motivated the development of noncommutative geometry.