ENGLISH

Basic Concepts of Synthetic Differential Geometry

By René Lavendhomme (auth.)

Book information

Publisher
Springer US
Year
1996
ISBN
079233941X, 9780792339410
DOI
10.1007/978-1-4757-4588-7
LCC
QA641 .L37 1996
Open Library ID
OL963985M
Language
english
Format
DJVU
Filesize
2 MB (1749502 bytes)
Series
Kluwer Texts in the Mathematical Sciences 13
Edition
1
Pages
320\168
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Differential Geometry; Category TheoryHomological Algebra; Mathematical Logic and Founda

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.

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