Definition
If X is a CW-complex with n-skeleton Xn, the cellular homology modules are defined as the homology groups of the cellular chain complex
The group
is free, with generators which can be identified with the n-cells of X. Let be an n-cell of X, let be the attaching map, and consider the composite maps
where is an -cell of X and the second map is the quotient map identifying to a point.
The boundary map
is then given by the formula
where is the degree of and the sum is taken over all -cells of X, considered as generators of .
Read more about this topic: Cellular Homology
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