Singular and Simplicial Homology Groups
DOI:
https://doi.org/10.53555/ephms.v7i8.1820Keywords:
Boundary operator, Simplicial complex, Singular homologyAbstract
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 .
Downloads
References
Allan J. Sieradski, An Introduction to Topology and Homotopy, PWS-Kent Publishing Company, Boston, 1992, 63-94.
Allen Hatcher, Algebraic Topology, Cambridge University Press, USA, 2002, 103-111.
Andrew H. Wallance, An Introduction to Algebraic Topology, Pergmon Press, New York, 2016, 175-183.
B. K. Lahiri, A First Course in Algebraic Topology, Alpha Science International Ltd, UK, 2000, 11-106.
D. Chatterjee, Topology. General and Algebraic, New Age International (p) Ltd, India, 2007, 146.
Glen E. Bredon, Topology and Geometry, Springer-Verlag, New York, Inc., 1993, 173.
James R. Munkres, Elements of Algebraic Topology, The Benjamin/ Cumming Publishing Company, Inc., California, 1984, 38-39.
James W. Vick, Homology Theory An Introduction to Algebraic Topology, 2end ed, Springer-Verlag, USA, 1994, 8-17.
M. S. Narasimhan - S. Ramanan - R. Sridharan - K. Varadarajan, Algebraic Topology, Tata Institute of Fundamental Research, Bombay, 2011, 29.
Mahima Ranjan Adhikari, Basic Algebraic Topology and Its Applications, Springer, India, 2016, 348.
Mikio Nakahara, Geometry. Topology and Physics, 2end ed, IOP Publishing Ltd, London, 2003, 118-125.
Steven H. Weintraub, Fundamentals of Algebraic Topology, Springer International Publishing, Switzerland, 2014, 2-57.
Tammo Tom Dieck, Algebraic Topology, European Mathematical Society Publishing House, Germany, 2008, 223-224.
V. V. Prasolov, Elements of Homology Theory, Volume 81, American Mathematical Society, USA, 2007, 11.
William Fulton, Algebraic Topology A First Course, Springer-Verlag, New York, 1995, 93.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212)

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
- All contributor(s) agree to transfer the copyright of this article to EPH Journal.
- EPH Journal will have all the rights to distribute, share, sell, modify this research article with proper reference of the contributors.
- EPH Journal will have the right to edit or completely remove the published article on any misconduct happening.