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Synthetic Differential Geometry

Anders Kock
Publisher: 
Cambridge University Press
Publication Date: 
2006
Number of Pages: 
233
Format: 
Paperback
Edition: 
2
Series: 
London Mathematical Society Lecture Note Series 333
Price: 
55.00
ISBN: 
0521687381
Category: 
Monograph
We do not plan to review this book.

 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.

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