Synthetic Differential Topology

by Marta Bunge, Felipe Gago, Ana María San Luis

Overview

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.

Product Details

ISBN-13:	9781108447232
Publisher:	Cambridge University Press
Publication date:	03/29/2018
Series:	London Mathematical Society Lecture Note Series , #448
Pages:	232
Product dimensions:	6.06(w) x 8.98(h) x 0.55(d)

About the Author

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

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

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.