Basic noncommutative geometry

by Khalkhali, Masoud

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Title Statements

Full title :Basic noncommutative geometry / Masoud Khalkhali.

Summary

"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--

Edition Statements

Publication Date:©2013
Edition:Second edition

Publication Statements

Publisher(s):European Mathematical Society
Place of Publication:Zurich, Switzerland
Language:eng
Publication Date:©2013

The Physical Object

Description:1 online resource (xviii, 239 pages) : : illustrations

Edition Identifiers

ISBN:9783037196281, 3037196289
oclc:ocn868203543
LC Classification:QC20.7.D52
Dewey Decimal:516.35

Examples of algebra-geometry correspondences -- Noncommutative quotients -- Cyclic cohomology -- Connes-Chern character -- Appendices: Gelfand-Naimark theorems -- Compact operators, Fredholm operators, and abstract index theory -- Projective modules -- Equivalence of categories.