Basic Concepts of Synthetic Differential Geometry

R. Lavendhomme (Autor)

Buch | Softcover

320 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1996
Springer-Verlag New York Inc.
978-1-4419-4756-7 (ISBN)

Artikel merken

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	19.11.2010
Reihe/Serie	Texts in the Mathematical Sciences ; 13
Zusatzinfo	XV, 320 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-4419-4756-6 / 1441947566
ISBN-13	978-1-4419-4756-7 / 9781441947567
Zustand	Neuware