Basic Concepts of Synthetic Differential Geometry

R. Lavendhomme (Autor)

Buch | Hardcover

320 Seiten

1996
Springer (Verlag)
978-0-7923-3941-0 (ISBN)

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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.

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..

Erscheint lt. Verlag	29.2.1996
Reihe/Serie	Texts in the Mathematical Sciences ; 13
Zusatzinfo	XV, 320 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-7923-3941-X / 079233941X
ISBN-13	978-0-7923-3941-0 / 9780792339410
Zustand	Neuware