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Jan, 2021
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Ordinary Homology and Cohomology

There are many textbooks for homology of simplicial complexes and singular homology of topological spaces. It is impossible to list all textbooks, each of which has its own pros and cons. And singular homology is just an example of a construction of one of various homology theories .

When I choose singular homology theory as a topic for senior’s seminar (reading course), I ask hand a list of important definitions and properties concerning singluar homology theory to students and ask them to go to the library and find them.

Thus I don’t have any particular favorite textbooks for elementary homology theory. I think, however, it is a good idea to read Dieudonné’s book [ Die89 ] , which explains the process of sophistication from Poincaré’s vague ideas into singular homology theory and generalized homology theories.