Smooth Manifolds and Observables by Jet Nestruev

Smooth Manifolds and Observables by Jet Nestruev

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.

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)

Jet Nestruev is a collective of authors, who originally convened for a seminar run by Alexandre Vinogradov at the Mechanics and Mathematics Department of Moscow State University in 1969. In the present edition, Jet Nestruev consists of Alexander Astashov (Senior Researcher at the State Research Institute of Aviation Systems), Alexandre Vinogradov (Professor of Mathematics at Salerno University), Mikhail Vinogradov (Diffiety Institute), and Alexey Sossinsky (Professor at the Independent University of Moscow).

SKU	NIN9780387955438
ISBN 13	9780387955438
ISBN 10	0387955437
Title	Smooth Manifolds and Observables
Author	Jet Nestruev
Series	Graduate Texts In Mathematics
Condition	New
Publisher	Springer-Verlag New York Inc.
Year published	2002-10-04
Number of pages	222
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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