Folding and Fundamental Groups of Flat Robertson-Walker Space
A. E. El-Ahmady · Indian Journal of Science and Technology · 2013
This paper aims to give a combinatorial characterization and also construct representations of the fundamental groups of the submanifolds on flat Robertson-Walker space by using some geometrical transformations. The homotopy groups of the limit folding on flat Robertson-Walker space are presented. The homotopy groups of the retractions and deformation retract on flat Robertson-Walker space are obtained. The fundamental groups of some types of geodesics in the flat Robertson-Walker space are discussed. New types of homotopy maps are deduced. Theorems governing this connection are achieved. Keywords: Flat Robertson-Walker space W4 , Homotopy Groups, Foldings, Retractions, Deformation Retracts. 2000 Mathematics Subject Classification: 53A35, 51H20, 57N10.