Homology Groups and Its Construction

  • Robert Marley Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi


This article explores the elementary ideas of boundary and homology theory that leads to homology groups. Taking the chain complex into account we would them to construct a general Homology Group and conclude with an additional definition for homology group.


W. Obeng-Denteh and S. Manu, “Essentials of topology in the contemporary times,” International Research Journal of Basic and Applied Science, vol. 4, pp. 27–30, 2012.

J. O. A. . W. Obeng-Denteh, “Topology: An overview.” Research Gate Publication 2017.

W. Obeng-Denteh, On the Study of Topological Dynamical Systems. PhD thesis, Kwame Nkrumah University of Science and Technology, 2012.

S. Eilenberg and H. P. Cartan, Homological algebra. Princeton University Press, 1956.

C. A. Weibel, History of homological algebra. na, 1999.

S. A. Morris, Topology Without Tears. University of New England, 2018.

E. H. Spanier, “Algebraic topology mcgraw-hill book co., new york toronto, ont,” 1966.

T. tom Dieck, Algebraic Topology. European Mathematical Societ, 2008.

A. Hatcher, Algebraic topology. Tsinghua University Press Ltd, 2005.

H. Miller, Algebraic Topology. MIT, 2018.

D. R. Wilkins, “Course 421 algedraic topology,” School of Mathematics, Trinity College, Dublin 2, Ireland, vol. 1, pp. 73 – 80, 1988 - 2008.