Connections on Microlinear Spaces

  • Ieke Moerdijk
  • Gonzalo E. Reyes

Abstract

One of the main new features of synthetic differential geometry, as opposed to classical geometry, is the existence of infinitesimal spaces such as D, D 2, D × D, etc. These spaces essentially allow us to give alternative, algebraic approaches to geometric notions which are classically defined by limit processes. For example, exterior differentiation of a form is interpreted geometrically via circulation along an n-cube, a notion which involves integrals. In Chapter IV, on the other hand, we saw how to define exterior differentiation via circulation along an infinitesimal n-cube, and no actual integration was needed in this definition.

Keywords

Vector Bundle Tangent Bundle Parallel Transport Affine Connection Connection Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Ieke Moerdijk
    • 1
  • Gonzalo E. Reyes
    • 2
  1. 1.Mathematical InstituteUniversity of UtrechtUtrechtThe Netherlands
  2. 2.Department of MathematicsUniversity of MontrealMontrealCanada

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