Cahiers Topos中流形的胶合
Gluing Manifolds in the Cahiers Topos
摘要：
我们表明，有一个完全忠实的嵌入到Cahiers拓扑，合成微分几何的首要模型之一的角流形的类别。这种嵌入被证明具有一些很好的性能，如开放的封面和横向纤维产品的保存。我们发展了一个理论，胶合流形角在卡希尔拓扑。在这种情况下，沿着一个共同的面与角的流形粘在一起的结果是一致的推出沿着一个无限加厚的面。我们的理论是为了在综合微分几何的背景下对未来的应用在域论。
英文摘要：
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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