Synthetic Differential Topology
eBook - PDF

Synthetic Differential Topology

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Synthetic Differential Topology

About this book

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.

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Table of contents

  1. Cover
  2. Series page
  3. Title page
  4. Copyright information
  5. Table of contents
  6. Preface
  7. Acknowledgements
  8. Introduction
  9. Part One Toposes and Differential Geometry
  10. Part Two Topics in SDG
  11. Part Three Toposes and Differential Topology
  12. Part Four Topics in SDT
  13. Part Five SDT and Differential Topology
  14. Part Six A Well Adapted Model of SDT
  15. References
  16. Index

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Yes, you can access Synthetic Differential Topology by Marta Bunge,Felipe Gago,Ana María San Luis in PDF and/or ePUB format, as well as other popular books in Mathematics & Logic in Mathematics. We have over one million books available in our catalogue for you to explore.