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.
| Autorius: | R. Lavendhomme |
| Serija: | Texts in the Mathematical Sciences |
| Leidėjas: | Springer US |
| Išleidimo metai: | 2010 |
| Knygos puslapių skaičius: | 340 |
| ISBN-10: | 1441947566 |
| ISBN-13: | 9781441947567 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Mathematical logic |
Parašykite atsiliepimą apie „Basic Concepts of Synthetic Differential Geometry“
