Smooth manifolds and observables

by
Jet Nestruev

Authors: A. M. Astashev, A. V. Bocharov, S. V. Duzhin, A. B. Sossinsky, A. M. Vinogradov, M. M. Vinogradov

Springer-Verlag, Graduate Texts in Mathematics, Vol. 220, 2002, XIII+222 pp., ISSBN 0-387-95543-7. Price: $59.95. In Europe for details and to order click here, in North America click here. Online version is available for Kluwer Online subscribers.
In this edition new exercises were added (mostly) to the first half of the book, thus achieving a better balance with the second half. Besides, some typos and minor errors, noticed in the Russian edition, were corrected.
Contents
Preface to the English Edition
Preface
Chapter 1
Introduction
Chapter 2
Cutoff and Other Special Smooth Functions on Rn
Chapter 3
Algebras and Points
Chapter 4
Smooth Manifolds (Algebraic Definition)
Chapter 5
Charts and Atlases
Chapter 6
Smooth Maps
Chapter 7
Equivalence of Coordinate and Algebraic Definitions
Chapter 8
Spectra and Ghosts
Chapter 9
The Differential Calculus as a Part of Commutative Algebra
Chapter 10
Smooth Bundles
Chapter 11
Vector Bundles and Projective Modules
Afterword
Appendix: A. M. Vinogradov
The Observability Principle, the Set Theory, and "Foundations of Mathematics"