Smooth Manifolds and Observables

Graduate Texts in Mathematics

Jet Nestruev

236 pages, parution le 20/11/2002

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Résumé

This book is a self-contained introduction to fiber spaces and differential operators on smooth manifolds that is accessible to graduate students specializing in mathematics and physics. 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 it will further the understanding of the mathematics underlying quantum field theory. The prerequisites for this book are a standard advanced calculus course as well as courses in linear algebra and algebraic structures.

Contents

Preface to English Edition

Introduction
Cutoff and other special smooth functions on R^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 a Commutative Algebra
Smooth bundles
Vector bundles and projective modules

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jet Nestruev
Parution	20/11/2002
Nb. de pages	236
Format	16 x 24
Couverture	Relié
Poids	487g
Intérieur	Noir et Blanc
EAN13	9780387955438
ISBN13	978-0-387-95543-8