Skip to content
Register Sign in Wishlist
Synthetic Differential Geometry

Synthetic Differential Geometry

2nd Edition

$79.95 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: July 2006
  • availability: Available
  • format: Paperback
  • isbn: 9780521687386

$ 79.95 (C)
Paperback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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 d2=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, first published in 2006, 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 categories and the interpretation of logical formulae within them. This is a second edition of Kock's classical text from 1981. Many notes have been included, with comments on developments in the field from the intermediate years, and almost 100 new bibliographic entries have been added.

    • Straightforward easy to read style with many exercises
    • No knowledge of differential geometry is presupposed
    • A much quoted classic now in 2nd edition, the two layers of the book (1981 and 2006) are clearly distinguished
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Edition: 2nd Edition
    • Date Published: July 2006
    • format: Paperback
    • isbn: 9780521687386
    • length: 246 pages
    • dimensions: 229 x 152 x 14 mm
    • weight: 0.37kg
    • contains: 4 b/w illus. 142 exercises
    • availability: Available
  • Table of Contents

    Preface to the second edition (2005)
    Preface to the first edition (1981)
    Part I. The Synthetic Ttheory:
    1. Basic structure on the geometric line
    2. Differential calculus
    3. Taylor formulae - one variable
    4. Partial derivatives
    5. Taylor formulae - several variables
    6. Some important infinitesimal objects
    7. Tangent vectors and the tangent bundle
    8. Vector fields
    9. Lie bracket
    10. Directional derivatives
    11. Functional analysis - Jacobi identity
    12. The comprehensive axiom
    13. Order and integration
    14. Forms and currents
    15. Currents - Stokes' theorem
    16. Weil algebras
    17. Formal manifolds
    18. Differential forms in terms of simplices
    19. Open covers
    20. Differential forms as quantities
    21. Pure geometry
    Part II. Categorical Logic:
    1. Generalized elements
    2. Satisfaction (1)
    3. Extensions and descriptions
    4. Semantics of function objects
    5. Axiom 1 revisited
    6. Comma categories
    7. Dense class of generators
    8. Satisfaction (2)
    9. Geometric theories
    Part III. Models:
    1. Models for axioms 1, 2, and 3
    2. Models for epsilon-stable geometric theories
    3. Well-adapted models (1)
    4. Well-adapted models (2)
    5. The algebraic theory of smooth functions
    6. Germ-determined T-infinity-algebras
    7. The open cover topology
    8. Construction of well-adapted models
    9. Manifolds with boundary
    10. Field property - germ algebras
    11. Order and integration in cahiers topos
    Appendices
    Bibliography
    Index.

  • Author

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

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×