Abstract
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.
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