Synthetic Differential Geometry

ISBN: 9780521687386 出版年：2006 页码：247 Anders Kock Cambridge University Press

Preface to the second edition (2005) Preface to the first edition (1981) Part I. The Synthetic Ttheory: 1. Basic structure on the geometric line 2. Differential calculus 3. Taylor formulae - one variable 4. Partial derivatives 5. Taylor formulae - several variables 6. Some important infinitesimal objects 7. Tangent vectors and the tangent bundle 8. Vector fields 9. Lie bracket 10. Directional derivatives 11. Functional analysis - Jacobi identity 12. The comprehensive axiom 13. Order and integration 14. Forms and currents 15. Currents - Stokes' theorem 16. Weil algebras 17. Formal manifolds 18. Differential forms in terms of simplices 19. Open covers 20. Differential forms as quantities 21. Pure geometry Part II. Categorical Logic: 1. Generalized elements 2. Satisfaction (1) 3. Extensions and descriptions 4. Semantics of function objects 5. Axiom 1 revisited 6. Comma categories 7. Dense class of generators 8. Satisfaction (2) 9. Geometric theories Part III. Models: 1. Models for axioms 1, 2, and 3 2. Models for epsilon-stable geometric theories 3. Well-adapted models (1) 4. Well-adapted models (2) 5. The algebraic theory of smooth functions 6. Germ-determined T-infinity-algebras 7. The open cover topology 8. Construction of well-adapted models 9. Manifolds with boundary 10. Field property - germ algebras 11. Order and integration in cahiers topos Appendices Bibliography Index.