Synthetic Differential Topology

Nonfiction, Science & Nature, Mathematics, Set Theory, Logic
Cover of the book Synthetic Differential Topology by Marta Bunge, Felipe Gago, Ana María San Luis, Cambridge University Press
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Author: Marta Bunge, Felipe Gago, Ana María San Luis ISBN: 9781108692205
Publisher: Cambridge University Press Publication: March 31, 2018
Imprint: Cambridge University Press Language: English
Author: Marta Bunge, Felipe Gago, Ana María San Luis
ISBN: 9781108692205
Publisher: Cambridge University Press
Publication: March 31, 2018
Imprint: Cambridge University Press
Language: English

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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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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