Other Properties
One sees from the cellular chain complex that the n-skeleton determines all lower-dimensional homology:
for k < n.
An important consequence of the cellular perspective is that if a CW-complex has no cells in consecutive dimensions, all its homology modules are free. For example, complex projective space CPn has a cell structure with one cell in each even dimension; it follows that for 0 ≤ k ≤ n,
and
Read more about this topic: Cellular Homology
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