Synthetic Geometry of Manifolds
Seiten
2009
Cambridge University Press (Verlag)
978-0-521-11673-2 (ISBN)
Cambridge University Press (Verlag)
978-0-521-11673-2 (ISBN)
This elegant book is certain to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. The clear presentation makes this tract ideal for graduate students and researchers wishing to familiarize themselves with the field.
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
Anders Kock is Professor Emeritus in the Department of Mathematical Sciences at Aarhus University, Denmark.
Preface; 1. Calculus and linear algebra; 2. Geometry of the neighbour relation; 3. Combinatorial differential forms; 4. The tangent bundle; 5. Groupoids; 6. Lie theory; non-abelian covariant derivative; 7. Jets and differential operators; 8. Metric notions; Appendix; Bibliography; Index.
| Reihe/Serie | Cambridge Tracts in Mathematics |
|---|---|
| Zusatzinfo | Worked examples or Exercises; 10 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 158 x 235 mm |
| Gewicht | 590 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 0-521-11673-2 / 0521116732 |
| ISBN-13 | 978-0-521-11673-2 / 9780521116732 |
| Zustand | Neuware |
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