Noncommutative Geometry

e-books in Noncommutative Geometry category

Deformations of Algebras in Noncommutative Geometry
by Travis Schedler - arXiv , 2015
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.
(7792 views)

Notes on Noncommutative Geometry
by Igor Nikolaev - arXiv , 2015
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.
(7699 views)

Very Basic Noncommutative Geometry
by Masoud Khalkhali - University of Western Ontario , 2004
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.
(9255 views)

Homological Methods in Noncommutative Geometry
by D. Kaledin , 2008
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.
(10212 views)

Surveys in Noncommutative Geometry
by Nigel Higson, John Roe - American Mathematical Society , 2006
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.
(11508 views)

An Introduction to Noncommutative Spaces and their Geometry
by Giovanni Landi - arXiv , 1997
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.
(14403 views)

An informal introduction to the ideas and concepts of noncommutative geometry
by Thierry Masson - arXiv , 2006
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.
(11148 views)

Noncommutative Geometry, Quantum Fields and Motives
by Alain Connes, Matilde Marcolli - American Mathematical Society , 2008
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.
(15469 views)

Noncommutative Geometry
by Alain Connes - Academic Press , 1994
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.
(16127 views)

Geometric Models for Noncommutative Algebra
by Ana Cannas da Silva, Alan Weinstein - University of California at Berkeley , 1998
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.
(11023 views)