Nikolaev, Igor V.
A Functorial Approach
Series:De Gruyter Studies in Mathematics 66
- An authoritative introductory treatment of noncommutative geometry
- A novel approach using functors is presented in detail
- Covers applications of the theory in topology, algebraic geometry, and number theory
Aims and Scope
This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field.
Part I: Basics
Categories and functors
Part II: Noncommutative invariants
Part III: Brief survey of NCG
Noncommutative algebraic geometry
Trends in noncommutative geometry
"The book is a good survey of noncommutative geometry, and is an excellent starting point for doing good research in the field. Each section of the book ends with a list of references for going deeply into each subject, and so this book gives a framework for the field of noncommutative geometry." Zentralblatt für Mathematik
"In any case, it is true with a vengeance that NCG is a big and important subject, and the book we are looking at here, with its subtitle of "A functorial approach" is doubtless a very valuable contribution on any number of counts, not the least of which being that the more functorial we get, the more generality we reap, and the clearer the overarching structure becomes. [...] In point of fact, the book under review is the first book on NCG to take a functorial approach as its Leitmotiv, and that is in itself a very solid contribution, pedagogically and mathematically." MAA Reviews