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  3. Synthetic Differential Topology
  • Cited by 4
Publisher:
Cambridge University Press
Online publication date:
March 2018
Print publication year:
2018
Online ISBN:
9781108553490
DOI:
https://doi.org/10.1017/9781108553490
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets, Geometry and Topology
Series:
London Mathematical Society Lecture Note Series (448)
Information

Book description

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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