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This paper presents an abstract approach of analysing population growth in the field of algebraic topology using the tools of homology theory. For a topological space   X   and any pointv    n    ∈  X   , wherev    nis the  n -dimensional surface, the group    η  =    X  ,    v    nis called population of the space   X  . The increasing sequence fromv  i  n   ∈  X    tov    jn    ∈  X    for    i  &lt;  j    provides the bases for the population growth. A growth in population    η  =    X  ,    v    noccurs ifv  i  n   &lt;   v  j  nfor allv    in    ∈  X    andv  j  n   ∈  X   . This is described by the homological invariant    Hη    k=  1   . The aim of this paper is to construct the homological invariant    Hη    kand use    Hη    k=  1    to analyse the growth of the population. This approach is based on topological properties such as connectivity and continuity. The paper made extensive use of homological invariant in presenting important information about the population growth. The most significant feature of this method is its simplicity in analysing population growth using only algebraic category and transformations.

Analytical Consideration of Growth in Population via Homological Invariant in Algebraic Topology