Ebooks for the Classroom+Faculty

Basic Concepts of Synthetic Differential Geometry
ISBN: 9781475745887
Platform/Publisher: SpringerLink / Springer US
Digital rights: Users: unlimited; Printing: unlimited; Download: unlimited
Subjects: Mathematics and Statistics;

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.