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