| Basic Concepts of Synthetic Differential Geometry Contributor(s): Lavendhomme, R. (Author) |
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ISBN: 1441947566 ISBN-13: 9781441947567 Publisher: Springer OUR PRICE: $208.99 Product Type: Paperback - Other Formats Published: November 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Algebra - General - Mathematics | Logic |
| Dewey: 511.3 |
| Series: Texts in the Mathematical Sciences |
| Physical Information: 0.7" H x 6.14" W x 9.21" (1.04 lbs) 320 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |