Connections on Microlinear Spaces

  • Ieke Moerdijk
  • Gonzalo E. Reyes


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.


Vector Bundle Tangent Bundle Parallel Transport Affine Connection Connection Versus 
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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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