𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Basic Concepts of Synthetic Differential Geometry

✍ Scribed by René Lavendhomme (auth.)

Book ID
127435378
Publisher
Springer
Year
1996
Tongue
English
Weight
2 MB
Edition
1
Category
Library
City
Dordrecht; Boston
ISBN
079233941X

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Subjects

Manifolds and Cell Complexes (incl. Diff.Topology)

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