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arXiv · 1002.3978

Differential Geometry of Microlinear Frolicher Spaces I

Hirokazu Nishimura
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Abstract

The central object of synthetic differential geometry is microlinear spaces. In our previous paper [Microlinearity in Frolicher spaces -beyond the regnant philosophy of manifolds-, International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have emancipated microlinearity from within well-adapted models to Frolicher spaces. Therein we have shown that Frolicher spaces which are microlinear as well as Weil exponentiable form a cartesian closed category. To make sure that such Frolicher spaces are the central object of infinite-dimensional differential geometry, we develop the theory of vector fields on them in this paper. The central result is that all vector fields on such a Frolicher space form a Lie algebra.

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Hirokazu Nishimura. 2010-02-22. Differential Geometry of Microlinear Frolicher Spaces I. https://arxiv.org/abs/1002.3978

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