By Alain Connes

This English model of the path-breaking French ebook in this topic offers the definitive therapy of the innovative method of degree thought, geometry, and mathematical physics constructed through Alain Connes. Profusely illustrated and invitingly written, this ebook is perfect for an individual who desires to comprehend what noncommutative geometry is, what it may do, or the way it can be utilized in numerous components of arithmetic, quantization, and simple debris and fields. Key gains* First complete remedy of the topic and its purposes* Written by way of the pioneer of this box* huge purposes in arithmetic* Of curiosity throughout such a lot fields* excellent as an creation and survey* Examples taken care of include:@subbul* the distance of Penrose tilings* the distance of leaves of a foliation* the gap of irreducible unitary representations of a discrete workforce* the part area in quantum mechanics* the Brillouin sector within the quantum corridor influence* A version of area time