Connections on Microlinear Spaces

Ieke Moerdijk and Gonzalo E. Reyes
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Ieke Moerdijk: University of Utrecht, Mathematical Institute
Gonzalo E. Reyes: University of Montreal, Department of Mathematics

Chapter Chapter V in Models for Smooth Infinitesimal Analysis, 1991, pp 181-237 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1991
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DOI: 10.1007/978-1-4757-4143-8_6

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