Synthetic Differential Geometry

Name: Synthetic Differential Geometry
Price: 81.29 USD
Availability: InStock
ISBN: 9780521687386

ISBN-10: 0521687381

ISBN-13: 9780521687386

Edition: 2nd 2006 (Revised)

Authors: Anders Kock, N. J. Hitchin

List price: $83.99

This item qualifies for FREE shipping.

30 day, 100% satisfaction guarantee!

Buy new: $81.29

Marketplace

2 new & used from $81.97

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

Description:

Synthetic Differential Geometry is a method of reasoning in differential geometry and differential calculus, based on the assumption of sufficiently many nilpotent elements on the number line, in particular numbers d such that d=0. The use of nilpotent elements allows one to replace the limit processes of calculus by purely algebraic calculations and notions. For the first half of the book familiarity with differential calculus and abstract algebra is presupposed during the development of results in calculus and differential geometry on a purely axiomatic/synthetic basis. In the second half basic notions of category theory are presumed in the construction of suitable Cartesian closed…

Book details

List price: $83.99
Edition: 2nd
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 6/22/2006
Binding: Paperback
Pages: 246
Size: 5.98" wide x 9.02" long x 0.55" tall
Weight: 0.814
Language: English

Anders Kock is an Associate Professor of Mathematics at the University of Aarhus, Denmark.



Preface to the Second Edition (2006)


Preface to the First Edition (1981)



The synthetic theory



Basic structure on the geometric line



Differential calculus



Higher Taylor formulae (one variable)



Partial derivatives



Higher Taylor formulae in several variables. Taylor series



Some important infinitesimal objects



Tangent vectors and the tangent bundle



Vector fields and infinitesimal transformations



Lie bracket - commutator of infinitesimal transformations



Directional derivatives



Functional analysis. Application to proof of Jacobi identity



The comprehensive axiom



Order-and integration



Forms and currents



Currents defined using integration. Stokes' Theorem



Weil algebras



Formal manifolds



Differential forms in terms of simplices



Open covers



Differential forms as quantities



Pure geometry



Categorical logic



Generalized elements



Satisfaction (1)



Extensions and descriptions



Semantics of function objects



Axiom 1 revisited



Comma categories



Dense class of generators



Satisfaction (2)



Geometric theories



Models



Models for Axioms 1, 2, and 3



Models for ?-stable geometric theories



Axiomatic theory of well-adapted models (1)



Axiomatic theory of well-adapted models (2)



The algebraic theory of smooth functions



Germ-determined T<sub>?</sub>-algebras



The open cover topology



Construction of well-adapted models



W-determined algebras, and manifolds with boundary



A field property of R and the synthetic role of germ algebras



Order and integration in the Cahiers topos


Appendices


Bibliography


Index