Download or read book Noncommutative Geometry And Physics 3 - Proceedings Of The Noncommutative Geometry And Physics 2008, On K-theory And D-branes & Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry written by Giuseppe Dito and published by World Scientific. This book was released on 2013-01-11 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics.