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.
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Illustrationen
Worked examples or Exercises; 2 Halftones, black and white; 21 Line drawings, black and white
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 13 mm
Gewicht
ISBN-13
978-1-108-44723-2 (9781108447232)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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 Maria San Luis is Professor of Mathematics at the University of Oviedo, Spain.
Autor*in
McGill University, Montreal
Universidade de Santiago de Compostela, Spain
Universidad de Oviedo, Spain
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.
