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arXiv · 1503.07408

Gluing Manifolds in the Cahiers Topos

Vincent S. Schlegel
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Abstract

We show that there is a fully faithful embedding of the category of manifolds with corners into the Cahiers topos, one of the premier models for Synthetic Differential Geometry. This embedding is shown to have a number of nice properties, such as preservation of open covers and transverse fibre products. We develop a theory for gluing manifolds with corners in the Cahiers topos. In this setting, the result of gluing together manifolds with corners along a common face is shown to coincide with a pushout along an infinitesimally thickened face. Our theory is designed with a view toward future applications in Field Theory within the context of Synthetic Differential Geometry.

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Vincent S. Schlegel. 2015-03-25. Gluing Manifolds in the Cahiers Topos. https://arxiv.org/abs/1503.07408

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