On Elastic Klein Bottle and Fundamental Groups

A. E. El-Ahmady^{*}

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References

[1] A. E. El-Ahmady, “Folding and Fundamential Groups of Buchdahi Space,” Indian Journal of Science and Technology, Vol. 6, No. 1, 2013, pp. 3940-3945.

[2] A. E. El-Ahmady, “On the Fundamential Group and Folding of Klein Bottle,” International Journal of Applied Mathematics and Statistics, Vol. 37, No. 6, 2013, pp. 56-64.

[3] A. E. El-Ahmady, “The Geodesic Deformation Retract of Klein Bottle and Its Folding,” International Journal of Nonlinear Science, Vol. 9, No. 3, 2011, pp. 1-8.

[4] A. E. El-Ahmady, “Retraction of Chaotic Black Hole,” The Journal of Fuzzy Mathematics, Vol. 19, No. 4, 2011, pp. 833-838.

[5] A. E. El-Ahmady, “Folding of Fuzzy Hypertori and Their Retractions,” Proceedings of the Mathematical and Physical Society of Egypt, Vol. 85, No. 1, 2007, pp. 1-10.

[6] A. E. El-Ahmady, “Limits of Fuzzy Retractions of Fuzzy Hyperspheres and Their Foldings,” Tamkang Journal of Mathematics, Vol. 37, No. 1, 2006, pp. 47-55.

[7] A. E. El-Ahmady, “The Variation of the Density Functions on Chaotic Spheres in Chaotic Space-Like Minkowski Space Time,” Chaos, Solitons and Fractals, Vol. 31, No. 5, 2007, pp. 1272-1278.
doi:10.1016/j.chaos.2005.10.112

[8] A. E. El-Ahmady, “Fuzzy Folding of Fuzzy Horocycle,” Circolo Matematico di Palermo Serie II, Tomo L III, 2004, pp. 443-450. doi:10.1007/BF02875737

[9] A. E. El-Ahmady, “Fuzzy Lobachevskian Space and Its Folding,” The Journal of Fuzzy Mathematics, Vol. 12, No. 2, 2004, pp. 609-614.

[10] A. E. El-Ahmady, “The Deformation Retract and Topological Folding of Buchdahi Space,” Periodica Mathematica Hungarica, Vol. 28, No. 1, 1994, pp. 19-30.
doi:10.1007/BF01876366

[11] A. E. El-Ahmady, “Folding of Some Types of Einstein Spaces,” The International Journal of Nonlinear Science, in Press.

[12] A. E. El-Ahmady and K. Al-Onema, “On the Folding of Lobachevsky Space,” International Journal of Applied Mathematics and Statistics, Vol. 4, No. 10, 2013, pp. 13-23.

[13] A. E. El-Ahmady, “The Deformation Retract and Topological Folding of the Schwarzchild Space,” Journal of Mathematical Physics, Vol. 25, No. 3, 1991.

[14] A. E. El-Ahmady and N. Al-Hazmi, “Retractions of One Dimensional Manifold,” Applied Mathematics, Vol. 3, No. 10, 2012, pp. 1135-1143.

[15] A. E. El-Ahmady and E. Al-Hesiny, “Folding and Deformation Retract of Hyperhelix,” Journal of Mathematics and Statistics, Vol. 8, No. 2, 2012, pp. 241-247.

[16] A. E. El-Ahmady and E. Al-Hesiny, “The Topological Folding of the Hyperbola in Minkowski 3-Space,” The International Journal of Nonlinear Science, Vol. 11, No. 4, 2011, pp. 451-458.

[17] A. E. El-Ahmady and A. S. Al-Luhaybi, “A Calculation of Geodesics in Flat Robertson-Walker Space and Its Folding,” International Journal of Applied Mathematics and Statistics, Vol. 33, No. 3, 2013, pp. 83-91.

[18] A. E. El-Ahmady and A. Al-Rdade, “A Geometrical Characterizations of Reissner-Nordstr?m Space Time and Its Retractions,” International Journal of Applied Mathematics and Statistics, Vol. 33, No. 3, 2013, pp. 83-91.

[19] A. E. El-Ahmady and A. S. Al-Luhaybi, “Ageometrical Characterization of Spatially Curved Robertson-Walker Space and Its Retractions,” Applied Mathematics, Vol. 3, No. 10, 2012, pp. 1153-1160.

[20] M. Reid and B. Szendroi, “Topology and Geometry,” Cambridge University Press, Cambridge, New York, 2005.

[21] M. Arkowitz, “Introduction to Homotopy Theory,” Springer-Verlage, New York, 2011.
doi:10.1007/978-1-4419-7329-0

[22] P. I. Shick, “Topology: Point-Set and Geometry,” Wiley, New York, 2007.

[23] J. Strom, “Modern Classical Homotopy Theory,” American Mathematical Society, 2011.