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Synthetic Geometry of Manifolds

Synthetic Geometry of Manifolds

£95.00

Part of Cambridge Tracts in Mathematics

  • Date Published: November 2009
  • availability: In stock
  • format: Hardback
  • isbn: 9780521116732

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  • 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.

    • Authored by one of the originators of synthetic geometry
    • A research monograph that can also be used as an invitation to differential geometry
    • Suitable for any mathematician interested in differential geometry
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    Reviews & endorsements

    'The book would certainly make a good graduate textbook. it is clearly written and contains a reasonable number of nontrivial exercises.' Zentralblatt MATH

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    Product details

    • Date Published: November 2009
    • format: Hardback
    • isbn: 9780521116732
    • length: 312 pages
    • dimensions: 235 x 158 x 24 mm
    • weight: 0.59kg
    • contains: 10 b/w illus. 40 exercises
    • availability: In stock
  • Table of Contents

    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.

  • Author

    Anders Kock, Aarhus Universitet, Denmark
    Anders Kock is Professor Emeritus in the Department of Mathematical Sciences at Aarhus University, Denmark.

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