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Connections on Microlinear Spaces

In: Models for Smooth Infinitesimal Analysis

Author

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  • Ieke Moerdijk

    (University of Utrecht, Mathematical Institute)

  • Gonzalo E. Reyes

    (University of Montreal, Department of Mathematics)

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.

Suggested Citation

  • Ieke Moerdijk & Gonzalo E. Reyes, 1991. "Connections on Microlinear Spaces," Springer Books, in: Models for Smooth Infinitesimal Analysis, chapter 0, pages 181-237, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-4143-8_6
    DOI: 10.1007/978-1-4757-4143-8_6
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