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Basic Concepts of Synthetic Differential Geometry

  • Book
  • © 1996

Overview

Authors:
  1. René Lavendhomme

    1. Université Catholique de Louvain, Belgium

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Part of the book series: Texts in the Mathematical Sciences (TMS, volume 13)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
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  2. Differential calculus and integrals

    • René Lavendhomme
    Pages 1-31

  3. Weil algebras and infinitesimal linearity

    • René Lavendhomme
    Pages 33-59

  4. Tangency

    • René Lavendhomme
    Pages 61-100

  5. Differential forms

    • René Lavendhomme
    Pages 101-140

  6. Connections

    • René Lavendhomme
    Pages 141-180

  7. Global actions

    • René Lavendhomme
    Pages 181-210

  8. On the algebra of the geometry of mechanics

    • René Lavendhomme
    Pages 211-267

  9. Note on toposes and models of S.D.G.

    • René Lavendhomme
    Pages 269-311

  10. Back Matter

    Pages 313-320
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Keywords

About this book

Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's theorem; the synthetic view of global action, going as far as the Weil characteristic homomorphism; the systematic account of structured Lie objects, such as Riemannian, symplectic, or Poisson Lie objects; the view of global Lie algebras as Lie algebras of a Lie group in the synthetic sense; and lastly the synthetic construction of symplectic structure on the cotangent bundle in general. Thus while the book is limited to a naive point of view developing synthetic differential geometry as a theory in itself, the author nevertheless treats somewhat advanced topics, which are classic in classical differential geometry but new in the synthetic context.
Audience: The book is suitable as an introduction to synthetic differential geometry for students as well as more qualified mathematicians.

Authors and Affiliations

  • Université Catholique de Louvain, Belgium

    René Lavendhomme

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