- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Volume:33
- On homology covering space and sheaf associated to the homology group
On homology covering space and sheaf associated to the homology group
Authors : Cengiz ULUÇAY
Pages : 0-0
Doi:10.1501/Commua1_0000000561
View : 32 | Download : 9
Publication Date : 1984-01-01
Article Type : Research Paper
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 insert ignore into journalissuearticles values(X); on X.Keywords : homology, space, associated
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