Folding and Fundamental Groups of Flat Robertson-Walker Space

A  E  El Ahmady

doi:10.17485/ijst/2013/v6i4.1

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Folding and Fundamental Groups of Flat Robertson-Walker Space

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2013/v6i4.1

Year: 2013, Volume: 6, Issue: 4, Pages: 1-8

Original Article

Folding and Fundamental Groups of Flat Robertson-Walker Space

A. E. El-Ahmady^*

Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt; [email protected]
*Author For Correspondence
A. E. El-Ahmady
Mathematics Department
Email:[email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

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.
Keywords: Flat Robertson-Walker space W4 , Homotopy Groups, Foldings, Retractions, Deformation Retracts. 2000 Mathematics Subject Classification: 53A35, 51H20, 57N10.