Vector Sheaves Associated with Principal Sheaves
摘要
In the framework of Abstract Differential Geometry, we show that to a given principal sheaf and a representation of its stuctural sheaf in , where A is a sheaf of associative, commutative, unital algebras (over R or C), we associate a vector sheaf. Moreover, under some natural assumptions on the compatibility of the representation with the Maurer-Cartan (or, logarithmic) differentials of the structural sheaves involved, we also show that the connections of the principal sheaf induce A-connections of the associated vector sheaf. We thus recover a result of the classical Differential Geometry within a purely algebro-topological context, without any smoothness assumption.
引用
@article{arxiv.math/9810083,
title = {Vector Sheaves Associated with Principal Sheaves},
author = {E. Vassiliou},
journal= {arXiv preprint arXiv:math/9810083},
year = {2013}
}
备注
LaTeX, 11 pages, to be published in the Proceedings of the 2nd Conference of Balkan Soc. of Geometers, Thessaloniki, 1998