An informal introduction to the ideas and concepts of noncommutative geometry
by Thierry Masson
Publisher: arXiv 2006
Number of pages: 56
This informal introduction is an extended version of a three hours lecture given at the 6th Peyresq meeting "Integrable systems and quantum field theory". In this text, we make an overview of some of the mathematical results which motivated the development of what is called noncommutative geometry.
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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 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 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 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.