Smooth manifolds and observables

Jet Nestruev

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

Textbook, MCCME, Moscow, 2000, 300 pp., ISSBN 5-900916-57-X (in Russian).

The book is available at the Independent University of Moscow (B. Vlasijevskij 11, bookstore at the ground floor, for details and to order click here) and at the FizMatKniga Web-Shop.

The second (electronic) edition is now available on-line. In this edition (likewise English one) 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 first edition, were corrected.

Chapter 1
Chapter 2
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
Differential calculus as an aspect of a commutative algebra
Chapter 10
Smooth bundles
Chapter 11
Vector bundles and projective modules
Appendix. A. M. Vinogradov
The observability principle, the set theory, and "foundations of mathematics"