Synthetic Differential Topology
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Synthetic Differential Geometry
Author: Anders Kock
language: en
Publisher: Cambridge University Press
Release Date: 2006-06-22
This book, first published in 2006, details how limit processes can be represented algebraically.
Synthetic Differential Topology
Author: Marta Bunge
language: en
Publisher: Cambridge University Press
Release Date: 2018-03-29
Represents the state of the art in the new field of synthetic differential topology.
Synthetic Geometry of Manifolds
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.