By Masoud Khalkhali
This publication offers an advent to noncommutative geometry and a few of its purposes. it may be used both as a textbook for a graduate path at the topic or for self-study. will probably be worthy for graduate scholars and researchers in arithmetic and theoretical physics and all those who find themselves drawn to gaining an knowing of the topic. One function of this publication is the wealth of examples and routines that support the reader to navigate in the course of the topic. whereas heritage fabric is supplied within the textual content and in different appendices, a few familiarity with uncomplicated notions of practical research, algebraic topology, differential geometry, and homological algebra at a first-year graduate point is beneficial. built via Alain Connes because the past due Nineteen Seventies, noncommutative geometry has came across many purposes to long-standing conjectures in topology and geometry and has lately made headways in theoretical physics and quantity conception. The publication starts off with an in depth description of a few of the main pertinent algebra-geometry correspondences by way of casting geometric notions in algebraic phrases, then proceeds to the assumption of a noncommutative area and the way it's built. The final chapters care for homological instruments: cyclic cohomology and Connes-Chern characters in $K$-theory and $K$-homology, culminating in a single commutative diagram expressing the equality of topological and analytic index in a noncommutative atmosphere. purposes to integrality of noncommutative topological invariants are given besides.
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