Notes on Noncommutative Geometry
by Igor Nikolaev
Publisher: arXiv 2015
Number of pages: 309
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. Our notes are intended for the graduate students and faculty with interests in noncommutative geometry; they can be read by non-experts in the field.
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by Nigel Higson, John Roe - American Mathematical Society
These lectures are 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, residue index theorem, etc.
by Alain Connes, Matilde Marcolli - American Mathematical Society
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.
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 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.