Synthetic differential topology / Marta Bunge, McGill University, Montreal, Felipe Gago, Universidade de Santiago de Compostela, Spain, Ana Maria San Luis, Universidad de Oviedo, Spain.

Format:

Book

Author/Creator:

Bunge, M. (Marta), author.

Gago Couso, Felipe, author.

San Luis Fernández, Ana María, author.

Series:

London Mathematical Society lecture note series ; 448.

London Mathematical Society lecture note series ; 448

Language:

English

Subjects (All):

Differential topology.

Geometry, Differential.

Mappings (Mathematics).

Physical Description:

1 online resource (ix, 223 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2018.

Summary:

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.

Notes:

Title from publisher's bibliographic system (viewed on 12 Mar 2018).

Includes bibliographical references and index.

ISBN:

1-108-69220-6

1-108-55349-4

1-108-56335-X