平行移动与函子
微分几何
2014-08-26 v5 范畴论
摘要
光滑纤维丛中联络的平行移动产生了一个从底流形的路径群胚到描述丛纤维的范畴的函子。我们通过引入两个概念来刻画由此类方式获得的函子：局部平凡化和光滑下降数据。这提供了一种用函子范畴替代带联络的光滑纤维丛范畴的方法。我们指出，这一概念可推广至范畴化丛中的联络，并说明了这种推广如何增进对高维平行移动的理解。
引用
@article{arxiv.0705.0452,
title = {Parallel Transport and Functors},
author = {Urs Schreiber and Konrad Waldorf},
journal= {arXiv preprint arXiv:0705.0452},
year = {2014}
}
评论
73 pages, 1 figure. Version 2 contains several improvements, in particular concerning the proofs of Lem. 2.15 and of Prop. 4.7, and the discussion in Appendix A2. Some notation has also been changed. Version 3 comes with an extended discussion of groupoid bundles with connection. Version 4 is the published version. In Version 5 we have replaced parts of the proof of Prop. 4.7 by better arguments