Some Algebraic Properties of Universal and Regular Covering Spaces

Authors: Ahmet Tekcan

Abstract:

Let X be a connected space, X be a space, let p : X -→ X be a continuous map and let (X, p) be a covering space of X. In the first section we give some preliminaries from covering spaces and their automorphism groups. In the second section we derive some algebraic properties of both universal and regular covering spaces (X, p) of X and also their automorphism groups A(X, p).

Keywords: covering space, universal covering, regular covering, fundamental group, automorphism group.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333070

References:

[1] Browder F.E. Covering Speces, Fibre Spaces and Local Homeomorphisms. Duke Math. Journal, 21(2)(1954), 329-336.
[2] Greenberg M.J. and Harper J.R. Algebraic Topology: A First Course. Addision-Wesley Publishing Company, Inc., 1980.
[3] Kosniovski C. A First Course in Algebraic Topology. Cambridge University Press, 1980.
[4] Massey W.S. Agebraic Topology An Introduction. Harcourt, Brace& World, Inc., 1967.
[5] Spanier E.H. Algebraic Topology. Tata McGraw-Hill Publishing Company Ltd. New Delhi, 1978.
[6] Tekcan A., Bayraktar M., and Bizim O. On the Covering Space and the Automorphism Group of the Covering Space. Balkan Journal of Geometry and Its Applications, 8(1)(2003), 101-108.