Singular and Simplicial Homology Groups

Authors

  • Hisham Ali Ahmed Ghanim
  • Mohammed Ali Bashir Hussein Department of Mathematics, Faculty of Mathematical Science and Statistics, Al Neelain University, Khartoum, Sudan
  • Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman Department of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman, Sudan

DOI:

https://doi.org/10.53555/ephms.v7i8.1820

Keywords:

Boundary operator, Simplicial complex, Singular homology

Abstract

     This paper identified the homology groups  of -simplex, -dimensional simplicial complex and -complex. We show that a -simplex  is a point or a vertex, -simplex  is a line or an edge, a -simplex  is defined to be a triangle with its interior included and a -simplex  is a solid tetrahedron. It is easy to continue to any -simplex . The aims of this paper are to construct and defined Singular Homology Groups and Simplicial Homology Groups in terms of -dimensional simplicial complex  and a topological space . We followed the historical analysis mathematical method. We found that simplexes are building blocks of polyhedron, both approaches yield the same results, and the homology groups  are quotient groups of -cycle groups  and -boundary groups .

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Published

2021-08-25

How to Cite

Ghanim, H. A. A. ., Bashir Hussein, M. A. ., & Abdel Rahman, A. R. A. R. A. G. . . (2021). Singular and Simplicial Homology Groups. EPH - International Journal of Mathematics and Statistics, 7(8), 01–10. https://doi.org/10.53555/ephms.v7i8.1820

Issue

Vol. 7 No. 8 (2021): EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212)

Section

Articles

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