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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/12895

Title: Application of homotopy to the ageing process of human body within the framework of algebraic topology
Authors: Brew, Lewis
Obeng-Denteh, William
Zigli, David Delali
Keywords: Abelian group
ageing
continuity
connectedness
homotopy
homology group
human body
homomorphism
topological space
Issue Date: 11-Jul-2019
Publisher: Canadian Center of Science and Education
Abstract: This paper presents the ageing process of the human body from thehomotopy conceptinthe algebraic topology. The compact connected human body with boundary is assumed to be topologically equivalent to a cylinder. The complexconnected cylindrical shape of the body x  S  I 1 , described by the functions f ,h : x  x is a Cartesian product of the vertical interval I  [0, ] and a circle 1 S . The initial state of the body x  S  I 1 is the topological shape of the infant. The ageing process called the homotopyisthe family of continuous functions f x t   on the interval I  [0,a] where a   and t   . It is an increasing sequence of the function f x t   of the body x  S  I 1 . The homotopy relates the topological shape of the infant tothe topological shape of the adult. The homology theory assigns to the human body  x a sequence of abelian groups H x n for n  0,1,2... and to the continuous function a sequence of homomorphism. The homology group characterizes the number and continuity of the compact surface of human body. The study excludes genetic, hormonal, environmental and other factors in the ageing process and recognizes the fact that ageing continues throughout life, through childhood, and adolescence into adulthood. Topologically the infant is equal to the adult since the infant continuously grows into the adult. The study found an algebraic way of relating homotopy to the process of ageing of human body. It was also established that this could offer other topologists useful topological tips in the application of homotopy to other physical continuous processes.
Description: An article published by Canadian Center of Science and Education and also available at doi:10.5539/jmr.v11n4p21
URI: http://hdl.handle.net/123456789/12895
Appears in Collections:College of Science

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