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.

Author: Anders Kock
Publisher: Cambridge University Press
Published: 11/19/2009
Pages: 312
Binding Type: Hardcover
Weight: 0.90lbs
Size: 8.90h x 5.90w x 0.50d
ISBN: 9780521116732

About the Author
Kock, Anders: - Anders Kock is Professor Emeritus in the Department of Mathematical Sciences at Aarhus University, Denmark.