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: Softcover reprint of the original 1st ed. 2003
Volume: 220
Dimensions:
Width: 15.50cm
, Height: 1.20cm
, Length: 23.50cm
Weight: 0.760kg
ISBN: 9781441930477
ISBN 10: 1441930477
Pages: 222
Publication Date: 03 December 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Replaced By: 9783030456498
Format: Paperback
Publisher's Status: Out of Print
Availability: In Print
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.
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)
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)
