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.
Produkt-Info
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Editions-Typ
Illustrationen
88
88 s/w Abbildungen
XVIII, 433 p. 88 illus.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 25 mm
Gewicht
ISBN-13
978-3-030-45652-8 (9783030456528)
DOI
10.1007/978-3-030-45650-4
Schweitzer Klassifikation
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).
<b>Jet Nestruev</b> 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).
Foreword.- Preface.- 1. Introduction.- 2. Cutoff and Other Special Smooth Functions on R^n.- 3. Algebras and Points.- 4. Smooth Manifolds (Algebraic Definition).- 5. Charts and Atlases.- 6. Smooth Maps.- 7. Equivalence of Coordinate and Algebraic Definitions.- 8. Points, Spectra and Ghosts.- 9. The Differential Calculus as Part of Commutative Algebra.- 10. Symbols and the Hamiltonian Formalism.- 11. Smooth Bundles.- 12. Vector Bundles and Projective Modules.- 13. Localization.- 14. Differential 1-forms and Jets.- 15. Functors of the differential calculus and their representations.- 16. Cosymbols, Tensors, and Smoothness.- 17. Spencer Complexes and Differential Forms.- 18. The (co)chain complexes that come from the Spencer Sequence.- 19. Differential forms: classical and algebraic approach.- 20. Cohomology.- 21. Differential operators over graded algebras.- Afterword.- Appendix.- References.- Index.
