Basic Concepts of Synthetic Differential Geometry (Texts in the Mathematical Sciences) [Hardcover]

R. Lavendhomme (Author)

Book Description

Publication Date: February 29, 1996 | ISBN-10: 079233941X | ISBN-13: 978-0792339410 | Edition: 1

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.

Product Details

• Hardcover: 336 pages
• Publisher: Springer; 1 edition (February 29, 1996)
• Language: English
• ISBN-10: 079233941X
• ISBN-13: 978-0792339410
• Product Dimensions: 9.4 x 6.5 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,535,078 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

4.0 out of 5 stars A Useful and Easy Introduction, May 9, 2000

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"jdfearns" (London) - See all my reviews

This review is from: Basic Concepts of Synthetic Differential Geometry (Texts in the Mathematical Sciences) (Hardcover)

This book is by far the most readable introduction to Synthetic Differential Geometry that there currently is. The book concentrates on building up axiomatic SDG with hardly a reference to ways of modelling it (ie: using topos theory), leaving the complicated mathematics until a good feeling for how SDG behaves is acquired. A good first read.