论文标题
几何共同体的基础：从共同方向到产品结构
Foundations of geometric cohomology: from co-orientations to product structures
论文作者
论文摘要
该手稿开发了一种几何方法，用于平滑歧管的普通共同体学，并基于带有角落的歧管的共同导向的平滑图构建了Cochain复合模型。特别注意这种平滑地图的撤回产品，该地图为我们的几何线圈提供了部分定义的产品结构，该结构诱导了杯子的共同体。还提供了同源性的平行处理，允许对违反和协方差理论进行几何统一。
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product of such smooth maps, which provides our geometric cochains with a partially defined product structure inducing the cup product in cohomology. A parallel treatment of homology is also given allowing for a geometric unification of the contravariant and covariant theories.
