The natural homology theory for CW complexes is cellular homology. Cellular homology theory is geometrically appealing at an intuitive level, but some technical subtleties are hidden in the theory and should be exposed to view for a thorough understanding. There are two ways of defining cellular homology: a formal way, given in terms of singular homology (Sects. 2.2, 2.3), and a geometrical way, in terms of incidence numbers and mapping degrees, given in Sect. 2.6 after an extensive discussion of degree and orientation in Sects. 2.4 and 2.5. The chapter ends with a presentation of the main points of homology in the cellular context.
KeywordsExact Sequence Chain Complex Short Exact Sequence Follow Diagram Commute Singular Homology
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