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.

Book Information
ISBN 9781108447232
Author Marta Bunge
Format Paperback
Page Count 232
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 360g