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140122 ||| eng |
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|a 9781475745887
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| 100 |
1 |
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|a Lavendhomme, R.
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| 245 |
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|a Basic Concepts of Synthetic Differential Geometry
|h Elektronische Ressource
|c by R. Lavendhomme
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| 250 |
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|a 1st ed. 1996
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| 260 |
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|a New York, NY
|b Springer US
|c 1996, 1996
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| 300 |
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|a XV, 320 p
|b online resource
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| 505 |
0 |
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|a 1 Differential calculus and integrals -- 2 Weil algebras and infinitesimal linearity -- 3 Tangency -- 4 Differential forms -- 5 Connections -- 6 Global actions -- 7 On the algebra of the geometry of mechanics -- 8 Note on toposes and models of S.D.G.
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Mathematical logic
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| 653 |
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|a Algebra, Homological
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| 653 |
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|a Manifolds and Cell Complexes
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| 653 |
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|a Category Theory, Homological Algebra
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| 653 |
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|a Manifolds (Mathematics)
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| 653 |
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|a Differential Geometry
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| 653 |
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|a Mathematical Logic and Foundations
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Texts in the Mathematical Sciences
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| 028 |
5 |
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|a 10.1007/978-1-4757-4588-7
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| 856 |
4 |
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|u https://doi.org/10.1007/978-1-4757-4588-7?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 516.36
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| 520 |
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|a 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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