Very Basic Noncommutative Geometry
by Masoud Khalkhali
Publisher: University of Western Ontario 2004
Number of pages: 104
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.
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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 Ana Cannas da Silva, Alan Weinstein - University of California at Berkeley
Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, like the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces.
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 Igor Nikolaev - arXiv
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. Intended for the graduate students and faculty with interests in noncommutative geometry; they can be read by non-experts.