Surveys in Noncommutative Geometry
by Nigel Higson, John Roe
Publisher: American Mathematical Society 2006
Number of pages: 208
The series of expository lectures intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Topics: applications of noncommutative geometry to problems in ordinary geometry and topology, Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory, residue index theorem of Connes and Moscovici, etc.
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by D. Kaledin
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.
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 Giovanni Landi - arXiv
These lectures notes are an introduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists.
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.