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Synthetic Differential Topology

$64.00 ( ) USD

Part of London Mathematical Society Lecture Note Series

  • Date Published: February 2018
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108563352

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  • This book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry which captures classical concepts of differential geometry and topology by means of the rich categorical structure of a necessarily non-Boolean topos and of the systematic use of logical infinitesimal objects in it. Beginning with an introduction to those parts of topos theory and synthetic differential geometry necessary for the remainder, this clear and comprehensive text covers the general theory of synthetic differential topology and several applications of it to classical mathematics, including the calculus of variations, Mather's theorem, and Morse theory on the classification of singularities. The book represents the state of the art in synthetic differential topology and will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.

    • Formally introduces synthetic differential topology
    • Contains the necessary background on topos theory and synthetic differential geometry
    • Of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology
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    Product details

    • Date Published: February 2018
    • format: Adobe eBook Reader
    • isbn: 9781108563352
    • contains: 23 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Introduction
    Part I. Toposes and Differential Geometry:
    1. Topos theory
    2. Synthetic differential geometry
    Part II. Topics in SDG:
    3. The Ambrose–Palais–Singer theorem in SDG
    4. Calculus of variations in SDG
    Part III. Toposes and Differential Topology:
    5. Local concepts in SDG
    6. Synthetic differential topology
    Part IV. Topics in SDT:
    7. Stable mappings and Mather's theorem in SDT
    8. Morse theory in SDT
    Part V. SDT and Differential Topology:
    9. Well-adapted models of SDT
    10. An application to unfoldings
    Part VI. A Well-Adapted Model of SDT:
    11. The Dubuc topos G
    12. G as a model of SDT
    References
    Index.

  • Authors

    Marta Bunge, McGill University, Montréal
    Marta Bunge is Professor Emerita of Mathematics at McGill University, Montreal. She is the author (with Professor Jonathon Funk) of the book Singular Coverings of Toposes (2010). Bunge is also a member of the editorial boards of the Cahiers de Topologie et Geometrie Differentielle Categoriques and of the Tbilisi Mathematical Journal.

    Felipe Gago, Universidade de Santiago de Compostela, Spain
    Felipe Gago is Professor of Mathematics at the University of Santiago de Compostela, Spain.

    Ana María San Luis, Universidad de Oviedo, Spain
    Ana María San Luis is Professor of Mathematics at the University of Oviedo, Spain.

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