Overview

This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.

Full Product Details

Author:   Jet Nestruev
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   220
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   1.150kg
ISBN:  

9780387955438

ISBN 10:   0387955437
Pages:   222
Publication Date:   04 October 2002
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Cutoff and Other Special Smooth Functions on ?n.- Algebras and Points.- Smooth Manifolds (Algebraic Definition).- Charts and Atlases.- Smooth Maps.- Equivalence of Coordinate and Algebraic Definitions.- Spectra and Ghosts.- The Differential Calculus as a Part of Commutative Algebra.- Smooth Bundles.- Vector Bundles and Projective Modules.

Reviews

From the reviews: Main themes of the book are manifolds, fibre bundles and differential operators acting on sections of vector bundles. ... A classical treatment of these topics starts with a coordinate description of a manifold M ... . The present book is based on an alternative point of view, where calculus on manifolds is treated as a part of commutative algebra. ... The book contains quite a few exercises and many useful illustrations. (EMS, September, 2004) The book provides a self-contained introduction to the theory of smooth manifolds and fibre bundles, oriented towards graduate students in mathematics and physics. The approach followed here, however, substantially differs from most textbooks on manifold theory. ... This book is certainly quite interesting and may appeal even to people who merely want to study algebraic geometry, in the sense that they will gain extra insight here by the attention which is paid to making certain constructions in algebraic geometry physically or intuitively acceptable. (Willy Sarlet, Zentralblatt MATH, Vol. 1021, 2003)

From the reviews: Main themes of the book are manifolds, fibre bundles and differential operators acting on sections of vector bundles. ! A classical treatment of these topics starts with a coordinate description of a manifold M ! . The present book is based on an alternative point of view, where calculus on manifolds is treated as a part of commutative algebra. ! The book contains quite a few exercises and many useful illustrations. (EMS, September, 2004) The book provides a self-contained introduction to the theory of smooth manifolds and fibre bundles, oriented towards graduate students in mathematics and physics. The approach followed here, however, substantially differs from most textbooks on manifold theory. ! This book is certainly quite interesting and may appeal even to people who merely want to study algebraic geometry, in the sense that they will gain extra insight here by the attention which is paid to making certain constructions in algebraic geometry physically or intuitively acceptable. (Willy Sarlet, Zentralblatt MATH, Vol. 1021, 2003)

From the reviews: Main themes of the book are manifolds, fibre bundles and differential operators acting on sections of vector bundles. ... A classical treatment of these topics starts with a coordinate description of a manifold M ... . The present book is based on an alternative point of view, where calculus on manifolds is treated as a part of commutative algebra. ... The book contains quite a few exercises and many useful illustrations. (EMS, September, 2004) The book provides a self-contained introduction to the theory of smooth manifolds and fibre bundles, oriented towards graduate students in mathematics and physics. The approach followed here, however, substantially differs from most textbooks on manifold theory. ... This book is certainly quite interesting and may appeal even to people who merely want to study algebraic geometry, in the sense that they will gain extra insight here by the attention which is paid to making certain constructions in algebraic geometry physically or intuitively acceptable. (Willy Sarlet, Zentralblatt MATH, Vol. 1021, 2003)

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions