Basic Concepts of Synthetic Differential Geometry

Released on by R. Lavendhomme
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  • Basic Concepts of Synthetic Differential Geometry Book Detail

  • Author : R. Lavendhomme
  • Release Date : 2013-03-09
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 331
  • ISBN 13 : 1475745885
  • File Size : 59,59 MB
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Basic Concepts of Synthetic Differential Geometry by R. Lavendhomme PDF Summary

Book 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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