On homology covering space and sheaf associated to the homology group

Year 1984, Volume: 33 , - , 01.01.1984

Cengiz Uluçay

https://doi.org/10.1501/Commua1_0000000561

Abstract

In this paper we consider a connected and locally arcvvise connected Hausdorff space X.
If N is a normal subgroup of the fundamental group F of X such that F / N is Abelian then it is shown that the normal covering space determined by N is the sheaf of the additive groups isomorphic to F / N at each point x G X as x runs through X, and conversely. It turns out that if, in particular, X is an analytic manifold of dimension n, then the homology covering space  determined by the homology group F / [F,F ] is itself an analytic complex manifold of dimen- sion n with the projection map TC :  -> X holomorphic. It follovvs at önce th at A is the sheaf A of germs of the totality of holomorphic functions A (X) on X.

Keywords

homology, space, associated

References

• Communications, Series A1:Mathematics and Statistics